Internal problem ID [15407]
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: 638.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 y^{\prime } \left (x +1\right )+6 y=6} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((3*x+2*x^2)*diff(y(x),x$2)-6*(1+x)*diff(y(x),x)+6*y(x)=6,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} x^{3}+c_{1} x +c_{1} +1 \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 20
DSolve[(3*x+2*x^2)*y''[x]-6*(1+x)*y'[x]+6*y[x]==6,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 x^3-c_2 (x+1)+1 \]