Internal problem ID [15412]
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: 643.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }-x y^{\prime }-3 y=5 x^{4}} \] 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: 18
dsolve([x^2*diff(y(x),x$2)-x*diff(y(x),x)-3*y(x)=5*x^4,1/x],singsol=all)
\[ y \left (x \right ) = \frac {c_{2} x^{4}+x^{5}+c_{1}}{x} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 21
DSolve[x^2*y''[x]-x*y'[x]-3*y[x]==5*x^4,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^5+c_2 x^4+c_1}{x} \]