OP Malhotra **Differential Equations** ISC Class-12 Maths Solutions Ch-17. Step by step Solutions of OP Malhotra SK Gupta, Anubhuti Gangal S.Chand ISC Class-12 Mathematics with Exe-17(a), Exe-17(b), Exe-17(c), Exe-17(d), Exe-17(e), Exe-17(f), Exe-17(g), Self Revision and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

## OP Malhotra Differential Equations ISC Class-12 Maths Solutions Ch-17

Class: | 12th |

Subject: | Mathematics |

Chapter : | Ch-17 Differential Equations of Section -A |

Board | ISC |

Writer | OP Malhotra, SK Gupta, Anubhuti Gangal |

Publications | S.Chand Publications 2020-21 |

**-: Included Topics :- **

Exe-17(a)

Exe-17(b)

Exe-17(c)

Exe-17(d)

Exe-17(e)

Exe-17(f)

Exe-17(g)

Self Revision

Chapter Test

### OP Malhotra Differential Equations ISC Class-12 Maths Solutions Ch-17

**Differential Equation :-**

An equation involving independent variable, dependent variable, derivatives of dependent variable with respect to independent variable and constant is called a differential equation.

e.g.

**Ordinary Differential Equation :-**

An equation involving derivatives of the dependent variable with respect to only one independent variable is called an ordinary differential equation.

e.g.

From any given relationship between the dependent and independent variables, a differential equation can be formed by differentiating it with respect to the independent variable and eliminating arbitrary constants involved.

**Order of a Differential Equation :-**

Order of a differential equation is defined as the order of the highest order derivative of the dependent variable with respect to the independent variable involved in the given differential equation.

Note: Order of the differential equation, cannot be more than the number of arbitrary constants in the equation.

**Degree of a Differential Equation :-**

The highest exponent of the highest order derivative is called the degree of a differential equation provided exponent of each derivative and the unknown variable appearing in the differential equation is a non-negative integer.

Note

(i) Order and degree (if defined) of a differential equation are always positive integers.

(ii) The differential equation is a polynomial equation in derivatives.

(iii) If the given differential equation is not a polynomial equation in its derivatives, then its degree is not defined.

**Exe-17(a)**

OP Malhotra Differential Equations ISC Class-12 Maths Solutions Ch-17

**Exe-17(b)**

### OP Malhotra Differential Equations ISC Class-12 Maths Solutions Ch-17

**Exe-17(c)**

Differential Equations ISC Class-12 Maths Solutions Ch-17

**Exe-17(d)**

### OP Malhotra Differential Equations ISC Class-12 Maths Solutions Ch-17

**Exe-17(e)**

OP Malhotra Differential Equations ISC Class-12 Maths Solutions Ch-17

**Formation of a Differential Equation :-**

**To form a differential equation from a given relation, we use the following steps:**

Step I: Write the given equation and see the number of arbitrary constants it has.

Step II: Differentiate the given equation with respect to the dependent variable n times, where n is the number of arbitrary constants in the given equation.

Step III: Eliminate all arbitrary constants from the equations formed after differentiating in step (II) and the given equation.

Step IV: The equation obtained without the arbitrary constants is the required differential equation.

**Solution of the Differential Equation :-**

A function of the form y = Φ(x) + C, which satisfies given differential equation, is called the solution of the differential equation.

**General Solution :-**

If the solution of the differential equation contains as many independent arbitrary constants as the order of the differential equation, then it is called the general solution or the complete integral of the differential equation.

e.g., The general solution of d^{2}y / dx^{2} + y = 0 is y = A cos x + B sin x because it contains two arbitrary constants A and B, which is equal to the order of the equation.

**Particular Solution :-**

Solution obtained by giving particular values to the arbitrary constants in the general solution is called a particular solution. e.g., In the

previous example, if A = B = 1, then y = cos x + sin x is a particular solution of the differential equation d^{2}y / dx^{2} + y = 0.

Solution of a differential equation is also called its primitive.

**Exe-17(f)**

OP Malhotra Differential Equations ISC Class-12 Maths Solutions Ch-17

**Exe-17(g)**

### OP Malhotra Differential Equations ISC Class-12 Maths Solutions Ch-17

**Self Revision**

Differential Equations ISC Class-12 Maths Solutions Ch-17

**Chapter Test**

### OP Malhotra Differential Equations ISC Class-12 Maths Solutions Ch-17

**-: End of Differential Equations**** S. Chand ISC Class-12 Maths Solution :-**

Return to :- OP Malhotra S. Chand ISC Class-12 Maths Solutions

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