75.6.3 problem 127

Internal problem ID [16759]
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 : 127
Date solved : Tuesday, January 28, 2025 at 09:21:27 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

\[ y = \left (x^{2}+c_{1} \right ) {\mathrm e}^{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 17

DSolve[D[y[x],x]-2*x*y[x]==2*x*Exp[x^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{x^2} \left (x^2+c_1\right ) \]