Internal problem ID [15415]
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: 646.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {\left (x^{4}-x^{3}\right ) y^{\prime \prime }+\left (2 x^{3}-2 x^{2}-x \right ) y^{\prime }-y=\frac {\left (x -1\right )^{2}}{x}} \] Given that one solution of the ode is \begin {align*} y_1 &= \frac {1}{x} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve([(x^4-x^3)*diff(y(x),x$2)+(2*x^3-2*x^2-x)*diff(y(x),x)-y(x)=(x-1)^2/x,1/x],singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{\frac {1}{x}} c_{1} x -\ln \left (x \right )+c_{2} +x}{x} \]
✓ Solution by Mathematica
Time used: 0.102 (sec). Leaf size: 27
DSolve[(x^4-x^3)*y''[x]+(2*x^3-2*x^2-x)*y'[x]-y[x]==(x-1)^2/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x-\log (x)+c_2 \left (-e^{\frac {1}{x}}\right ) x+c_1}{x} \]