75.20.8 problem 643

Internal problem ID [17142]
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 ODEs). Section 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 643
Date solved : Tuesday, January 28, 2025 at 09:54:08 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }-3 y&=5 x^{4} \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=\frac {1}{x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (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)
 

\[ y = \frac {c_{2} x^{4}+x^{5}+c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 21

DSolve[x^2*D[y[x],{x,2}]-x*D[y[x],x]-3*y[x]==5*x^4,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^5+c_2 x^4+c_1}{x} \]