Differential Equations Class 12 OP Malhotra Exe-17A Maths Solutions. In this article you would learn about order and degree of differential equations . Step by step solutions of latest textbook has been given as latest syllabus. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.
Differential Equations Class 12 OP Malhotra Exe-17A ISC Maths Solutions Ch-17
| Board | ISC |
| Publications | S Chand |
| Subject | Maths |
| Class | 12th |
| Chapter-17 | Differential Equations |
| Writer | OP Malhotra |
| Exe-17(a) | Order and Degree of Differential Equations |
Order and degree of differential equations
Indefinite Integrals Class 12 OP Malhotra Exe-17A Solutions
Que-1: dy/dx = sin x
Sol: Given differential eqn. be,
dy/dx = sin x
Here, order of highest ordered derivative existing in diff. eqn. be 1 and its power be 1,
∴ order of differential eqn. be 1 and degree of differential eqn. be 1.
Que-2: x²(dy/dx)² + 2y²x = 0
Sol: Given diff. eqn. be,
x²(dydx)² + 2y²x = 0
Here the order of highest ordered derivative existing in diff. eqn. be 1. The exponent of highest ordered derivative be 2.
∴ Order and degree of diff. eqn. be 1 and 2.
Que-3: d²y/dx²−3(dy/dx)² + x = 0
Sol: Given diff. eqn. be,
d²y/dx²−3(dy/dx)² + x = 0
The highest ordered derivative existing in differential eqn. be d²y/dx² and its order be 2.
∴ order of given diff. eqn. be 2. The exponent of highest ordered derivative be 1.
∴ degree of given diff. eqn. be 1.
Que-4: (d²y/dx²)²+dy/dx – xy = 0
Sol: Given differential eqn. be
(d²y/dx²)²+dy/dx – xy = 0
Here, the order of the highest ordered derivative existing in the differential eqn. be 2 and its power 2.
Thus, order of given diff. eqn. be 2 and degree of given differential eqn. be 2.
Que-5: d³y/dx³−5d²y/dx²+(dy/dx)4-5x = 0
Sol: Given differential eqn. be,
d³y/dx³−5d²y/dx²+(dy/dx)4-5x = 0
Here the highest ordered derivative existing in given diff., eqn. be d³y/dx³ and its order be 3. Thus order of given diff. eqn. be 3. The power of d³y/dx³ in given diff. eqn. be 1. Thus degree of given diff. eqn. be 1.
Que-6: y = x dy/dx+a/(dy/dx)
Sol: Given differential eqn. can be written as xdydx+adydx
y(dy/dx) = x(dy/dx)² + a
Here the order of highest ordered derivative existing in diff. eqn. be 1 and its power be 2.
Thus order of given diff. eqn. be 1.
and the degree of given diff. eqn. be 2.
Que-7: (√a+x)(dy/dx) + x = 0
Sol: The given diff. eqn. be,
(√a+x)(dy/dx) + x = 0
Here, the order of highest ordered derivative existing in diff. eqn. be 1 and its power be also equal to 1.
Thus, order of given diff. eqn. be 1 and its degree be also equal to 1.
Que-8: x√1−y² dx + y√1−x² dy = 0
Sol: Given differential eqn. can be written as :
x√1−y² dx + y√1−x² dy = 0
Here, the order of highest ordered derivative existing in given diff. eqn. be 1 and its power be also 1.
Thus order of given differential eqn. be 1 and degree of given diff. eqn. be 1.
Que-9: [1+(dy/dx)²]3/2=5 d²y/dx²
Sol: Given diff. eqn. be,
[1+(dy/dx)²]3/2=5 d²y/dx²;
On squaring both sides ; we have
[1+(dy/dx)2]³=25(d²y/dx²)²
Here the order of highest ordered derivative existing in given diff. eqn. be 2 and its power be equal to 2. Hence the order and degree of given diff. eqn. be 2 and 2.
Que-10: y = x dy/dx+a√(1+(dy/dx)²)
Sol: Given diff. eqn. be written as,
y = x dy/dx+a√(1+(dy/dx)²);
On squaring ; we have
(y−x dy/dx)²=a²[1+(dy/dx)²]
Here the order of highest ordered derivative existing in diff. eqn. be 1 and its power be 2.
∴ order of given diff. eqn. be 1. and the degree of given diff. eqn. be 2.
Que-11: (d²y/dx²)²=(dy/dx)²
Sol: Given diff. eqn. can be written as,
(d²y/dx²)²=(dy/dx)²
Here, the order of the highest ordered derivative existing in the diff. eqn. be 2 and its power be 3.
Thus the order of given diff. eqn. be 2 and degree of given diff. eqn. be 3.
Que-12: dy/dx=x / (dy/dx)
Sol: Given differential eqn. can be written as
(dy/dx)² = x
Here the order of highest ordered derivative existing in given diff. eqn. be 1 and its power be 2.
Thus, the order of given diff. eqn. be 1 and degree of given differential eqn. be 2.
–: End of Differential Equations Class 12 OP Malhotra Exe-17A ISC Math Ch-17 Solution :–
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