75.4.33 problem 98

Internal problem ID [16735]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
Problem number : 98
Date solved : Tuesday, January 28, 2025 at 09:20:06 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 x \left (\pi +y\right ) \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x)=2*x*(Pi+y(x)),y(x), singsol=all)
 

\[ y = -\pi +{\mathrm e}^{x^{2}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 24

DSolve[D[y[x],x]==2*x*(Pi+y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\pi +c_1 e^{x^2} \\ y(x)\to -\pi \\ \end{align*}