Internal problem ID [15402]
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 15.4 Nonhomogeneous linear equations with
constant coefficients. The Euler equations. Exercises page 143
Problem number: 633.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y=2 \ln \left (x \right )^{2}+12 x} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {c_{2}}{x^{2}}+2 x +\frac {7}{2}+\frac {c_{1}}{x}-3 \ln \left (x \right )+\ln \left (x \right )^{2} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 32
DSolve[x^2*y''[x]+4*x*y'[x]+2*y[x]==2*(Log[x])^2+12*x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1}{x^2}+2 x+\log ^2(x)-3 \log (x)+\frac {c_2}{x}+\frac {7}{2} \]