Internal problem ID [15430]
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 ODE’s). Section 15.5 Linear equations with variable coefficients.
The Lagrange method. Exercises page 148
Problem number: 665.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }=-4 x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {\left (-2 x -1\right ) c_{1} {\mathrm e}^{-2 x}}{4}-x^{2}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.126 (sec). Leaf size: 35
DSolve[x*y''[x]+(2*x-1)*y'[x]==-4*x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2-\frac {1}{4} e^{-2 x} \left (4 e^{2 x} x^2+2 c_1 x+c_1\right ) \]