Internal problem ID [15053]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page
54
Problem number: 160.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }+3 y x -y \,{\mathrm e}^{x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve(diff(y(x),x)+3*x*y(x)=y(x)*exp(x^2),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{-\frac {3 x^{2}}{2}+\frac {\sqrt {\pi }\, \operatorname {erfi}\left (x \right )}{2}} \]
✓ Solution by Mathematica
Time used: 0.075 (sec). Leaf size: 33
DSolve[y'[x]+3*x*y[x]==y[x]*Exp[x^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{\frac {1}{2} \left (\sqrt {\pi } \text {erfi}(x)-3 x^2\right )} \\ y(x)\to 0 \\ \end{align*}