Internal problem ID [15417]
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: 648.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x \left (x -1\right ) y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y=\left (2 x -3\right ) x^{2}} \] Given that one solution of the ode is \begin {align*} y_1 &= x^{2} \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve([x*(x-1)*diff(y(x),x$2)-(2*x-1)*diff(y(x),x)+2*y(x)=x^2*(2*x-3),x^2],singsol=all)
\[ y \left (x \right ) = c_{2} x^{2}+x^{3}-2 c_{1} x +c_{1} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 40
DSolve[x*(x-1)*y''[x]-(2*x-1)*y'[x]+2*y[x]==x^2*(2*x-3),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^3+\left (-\frac {1}{2}+c_1\right ) x^2+(1-2 c_1+c_2) x-\frac {1}{2}+c_1-\frac {c_2}{2} \]