Solve: dy / dx = x2 e-3y given that y = 0 when x = 0 The answer - Maths - Differential Equations

Question

Solve:
dy / dx = x2 e-3y given that y = 0 when x
= 0
The answer given in the book is : e3y = x3
+ 1

Varun.Rawat · Accepted Answer

The given differential equation is,dydx = x2 e-3y⇒dye-3y = x2
dx variable separable⇒e3y dy = x2 dxIntegrating both sides,
we get∫e3y dy = ∫x2 dx⇒e3y3 = x33 + C 1put x = 0
and y = 0 in 1, we get13 = 0 + C⇒C = 13putting the value of C
in1, we gete3y3 = x33 + 13⇒e3y = x3 + 1

Solve: dy / dx = x2 e-3y . given that y = 0 when x = 0 The answer given in the book is : e3y = x3 + 1

Solve:

dy / dx = x² e^-3y . given that y = 0 when x = 0

The answer given in the book is : e^3y = x³ + 1