Class 12

Math

Calculus

Differential Equations

Find the particular solution of the differential equation $dxdy =−4xy_{2}$given that $y=1$, when$x=0$.

$y_{2}dy =−4xdx$

integrating both side

$−y_{−1}=−42x_{2} +c$

$y_{−1}−2x_{2}+C=0(1)$

given y=1 and x=0

1-0+C=0

C=-1

putting this value in equation (1)

$y_{−1}−2x_{2}−1=0$