AP EAMCET2016MathematicsDifferential Equations
The solution of the differential equation (1+y^2 )+ (x-e^ ⁻¹ y ) d y d x =0 , is
Options
- Ax e^ ⁻¹ y = ^ -1 y +C
- Bx e^ 2 ⁻¹ y =e^ - ⁻¹ y +C
- C2 x e^ ⁻¹ y =e^ 2 ⁻¹ y +C
- Dx^2 e^ ⁻¹ y =4 e^ 2 ⁻¹ y +C
Correct answer
C. 2 x e^ ⁻¹ y =e^ 2 ⁻¹ y +C
Step-by-step solution
Given differential equation, aligned & (1+y^2 ) (x-e^ ⁻¹ y ) d y d x =0 & d y d x + x 1+y^2 = e^ ⁻¹ y 1+y^2 & P= x 1+y^2 , Q = e^ ⁻¹ y 1+y^2 aligned Now, integration factor, IF =e^ p d y =e^ l 1 1+y^2 d y =e^ ⁻¹ y The solution of differential equation, aligned & x . I F= Q . I F d y+C & x e^ ⁻¹ y = e^ 2 ⁻¹ y 1+y^2 d y+C & x e^ ⁻¹ y = e^ 2 ⁻¹ y 1+y^2 +C & 2 x e^ ⁻¹ y =e^ 2 ⁻¹ y +C aligned