75.19.16 problem 633

Internal problem ID [17132]
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 15.4 Nonhomogeneous linear equations with constant coefficients. The Euler equations. Exercises page 143
Problem number : 633
Date solved : Tuesday, January 28, 2025 at 09:53:54 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&=2 \ln \left (x \right )^{2}+12 x \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(x^2*diff(y(x),x$2)+4*x*diff(y(x),x)+2*y(x)=2*(ln(x))^2+12*x,y(x), singsol=all)
 

\[ y = \frac {c_{2}}{x^{2}}+2 x +\frac {7}{2}+\frac {c_{1}}{x}-3 \ln \left (x \right )+\ln \left (x \right )^{2} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 32

DSolve[x^2*D[y[x],{x,2}]+4*x*D[y[x],x]+2*y[x]==2*(Log[x])^2+12*x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1}{x^2}+2 x+\log ^2(x)-3 \log (x)+\frac {c_2}{x}+\frac {7}{2} \]