77.1.140 problem 167 (page 240)

Internal problem ID [18030]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 167 (page 240)
Date solved : Tuesday, January 28, 2025 at 11:23:02 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 32

dsolve(x^3*diff(y(x),x$3)-x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-2*y(x)=x^3+3*x,y(x), singsol=all)
 

\[ y = \frac {\left (-12-6 \ln \left (x \right )^{2}+4 \left (-3+c_{3} \right ) \ln \left (x \right )+x^{2}+4 c_{2} x +4 c_{1} \right ) x}{4} \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 39

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

\[ y(x)\to \frac {1}{4} x \left (x^2-6 \log ^2(x)+4 c_3 x+4 (-3+c_2) \log (x)+4 (-3+c_1)\right ) \]