77.1.113 problem 141 (a) (page 205)

Internal problem ID [18003]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 141 (a) (page 205)
Date solved : Tuesday, January 28, 2025 at 08:28:28 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.069 (sec). Leaf size: 21

dsolve((x^2+2)*diff(y(x),x$3)-2*x*diff(y(x),x$2)+(x^2+2)*diff(y(x),x)-2*x*y(x)=x^4+12,y(x), singsol=all)
 

\[ y = x^{3}+c_{1} x^{2}+\cos \left (x \right ) c_{2} +c_{3} \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.971 (sec). Leaf size: 46

DSolve[(x^2+2)*D[y[x],{x,3}]-2*x*D[y[x],{x,2}]+(x^2+2)*D[y[x],x]-2*x*y[x]==x^4+12,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^3+\frac {c_1 x^2}{2}+\frac {1}{2} i c_2 e^{-i x}-\frac {1}{4} c_3 e^{i x} \]