75.20.26 problem 665

Internal problem ID [17160]
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 : 665
Date solved : Tuesday, January 28, 2025 at 09:54:48 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

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

\[ y = \frac {\left (-2 x -1\right ) c_{1} {\mathrm e}^{-2 x}}{4}-x^{2}+c_{2} \]

✓ Solution by Mathematica

Time used: 2.205 (sec). Leaf size: 42

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

\begin{align*} y(x)\to \int _1^x\left (e^{-2 K[1]} c_1-2\right ) K[1]dK[1]+c_2 \\ y(x)\to -x^2+1+c_2 \\ \end{align*}