75.20.23 problem 662

Internal problem ID [17157]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 662
Date solved : Tuesday, January 28, 2025 at 09:54:42 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }&=4 x^{3} {\mathrm e}^{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

dsolve(x*diff(y(x),x$2)-(1+2*x^2)*diff(y(x),x)=4*x^3*exp(x^2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.074 (sec). Leaf size: 25

DSolve[x*D[y[x],{x,2}]-(1+2*x^2)*D[y[x],x]==4*x^3*Exp[x^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{x^2} \left (x^2-1+\frac {c_1}{2}\right )+c_2 \]