75.6.27 problem 160

Internal problem ID [16783]
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
Date solved : Tuesday, January 28, 2025 at 09:22:35 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+3 y x&=y \,{\mathrm e}^{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 20

dsolve(diff(y(x),x)+3*x*y(x)=y(x)*exp(x^2),y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{-\frac {3 x^{2}}{2}+\frac {\sqrt {\pi }\, \operatorname {erfi}\left (x \right )}{2}} \]

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 33

DSolve[D[y[x],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*}