Let be a differentiable function satisfying dy dx =x^ 2 e^ y

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

Let

y=y(x)

be a differentiable function satisfying

\frac{dy}{dx}=x^{2}e^{y}.

The solution curve intersects the

y

-axis at the point where

y=\ln 2

. (a) Derive the general solution for

y

in terms of

x

. (b) Use the information about the intersection with the

y

-axis to determine the particular solution. (c) Verify directly, by differentiation, that your particular solution satisfies the original differential equation.

Related theory

Modeling
Separation of Variables
Solutions
Variable separable equations
Differential equations with variables separable
Differential Equations

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