Solving Homogeneous Differential Equation Class 12 OP Malhotra Exe-17E Maths Solutions. In this article you would learn about solving homogeneous equation. 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.
Solving Homogeneous Differential Equation Class 12 OP Malhotra Exe-17E ISC Maths Solutions Ch-17
| Board | ISC |
| Publications | S Chand |
| Subject | Maths |
| Class | 12th |
| Chapter-17 | Differential Equations |
| Writer | OP Malhotra |
| Exe-17(e) | Solving Homogeneous Equation |
Solving Homogeneous Differential Equation
Differential Equations Class 12 OP Malhotra Exe-17e Solutions
Que-1: 2xy dy/dx = x² + y²
Sol: Given 2xy dy/dx = x² + y²
Que-2: x²dy/dx = 2xy + y²
Sol:
Que-3: x²dy/dx = x² + 5xy + 4y²
Sol:
Que-4: x²dy/dx = y(x + y)
Sol:
Que-5: y² + x²dy/dx = xy dy/dx
Sol:
Que-6: x²dy/dx = (x² – 2y² + xy)
Sol:
Que-7: x²y dx = (x³ + y³)dy
Sol:
Que-8: dy/dx = y/x + tany/x
Sol: Given dy/dx=y/x+tanyx=ϕ(y/x) … (1)
which is homogeneous differential equation.
put y = vx ⇒ dy/dx = v + xdv/dx
∴ from eqn. (1); we have
v + x dv/dx = v + tan v ⇒ xdv/dx = tan v
⇒ dv/tanv = dx/x ; on integratmg ; we have
∫ cot v dv = ∫dx/x + logc
⇒ log | sin v | = log | x | + log c
⇒ sin v = cx ⇒ sin (y/x) = cx
be the required solution.
Que-9: [x√(x²+y²)−y²]dx + xy dy = 0
Sol: Given differential equation can be written as :
![Que-9: [x√(x²+y²)−y²]dx + xy dy = 0](https://icsehelp.com/wp-content/uploads/2025/10/5-300x300.png)
Que-10: (x² – 3xy²)dx = (y³ – 3x²y)dy
Sol: Given diff. eqn. can be written as dy/dx=x³−3xy²/y³−3x²y … (1)
which is homogeneous diff. eqn.
Que-11: dy/dx=y/x+siny/x
Sol: Given dy/dx=y/x+siny/x … (1)
which is homogeneous diff. eqn.
put y = vx ⇒ dy/dx = v + xdv/dx
∴ from (1); we have
which is the required solution.
Que-12: x(dy/dx) = y(log y – log x + 1)
Sol: Given diff. eqn. can be written as ;
Que-13: x² dy + y (x + y) dx = 0, given that y = 1 when x = 1.
Sol: Given diff. eqn. can be written as ;
x²dy + y(x + y)dx = 0
Que-14: dy/dx=xy/x²+y² given that y = 1 when x = 0.
Sol: Given diff. eqn. be,
dy/dx=xy/x²+y² … (1)
which is homogeneous diff. eqn.
put y = vx ⇒ dy/dx = v + xdv/dx
∴ from (1) ; we have
given that y = 1, when x = 0
∴ from (2) ; we have
0 + log 1 = c ⇒ x = 0
Thus eqn. (2) becomes ;
– x²/2y² ⇒ log y = x²/2y²
⇒ y = e^(x²/2y²)
be the required particular solution.
Que-15: Find the particular solution of the differential equation 2yex/ydx + (y – 2xex/y)dy = 0 given that x = 0, when y = 1.
Sol: Given diff. eqn. can be written as,
given that x = 0 when y = 1
∴ from (2); we have 2 = c
∴ from (2); we have 2ex/y= – log | y| + 2
⇒ex/y = – 1/2 log|y| + 1
which is the required solution.
–: End of Solving Homogeneous Differential Equation Class 12 OP Malhotra Exe-17E Maths Solutions :–
Return to :- OP Malhotra ISC Class-12 S Chand Publication Maths Solutions
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