40.12.4 problem 9

Internal problem ID [6752]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 17. Linear equations with variable coefficients (Cauchy and Legndre). Supplemetary problems. Page 110
Problem number : 9
Date solved : Monday, January 27, 2025 at 02:27:31 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 26

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

\[ y = \frac {x \left (9 c_2 \ln \left (x \right )^{2}+x^{3}+9 c_3 \ln \left (x \right )+9 c_1 \right )}{9} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 31

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

\[ y(x)\to \frac {x^4}{9}+c_1 x+c_3 x \log ^2(x)+c_2 x \log (x) \]