Match the following differential equations with their solutions.
The symbols $A$, $B$, $C$ in the solutions stand for arbitrary constants.
You must get all of the answers correct to receive credit.

1. $\frac{d^2y}{dx^2}+4 y =0$
2. $\frac{dy}{dx}=\frac{-2xy}{x^2- 2 y^2}$
3. $\frac{d^2y}{dx^2}+14\frac{dy}{dx}+49 y=0$
4. $\frac{dy}{dx}= 4 xy$
5. $\frac{dy}{dx}+21 x^2y = 21 x^2$

A. $y = A\cos(2 x) + B\sin(2 x)$
B. $y= Ce^{-7 x^3}+1$
C. $y = A e^{2 x^2}$
D. $3yx^2 - 2 y^3 = C$
E. $y = A e^{-7 x} + B xe^{-7 x}$