56.3.15 problem 15

Internal problem ID [8873]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 15
Date solved : Monday, January 27, 2025 at 05:11:25 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y&=1 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 24

dsolve(x^4*diff(y(x),x$2)+x^3*diff(y(x),x)-4*x^2*y(x)=1,y(x), singsol=all)
 

\[ y = \frac {16 c_{2} x^{4}-4 \ln \left (x \right )+16 c_{1} -1}{16 x^{2}} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 29

DSolve[x^4*D[y[x],{x,2}]+x^3*D[y[x],x]-4*x^2*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {16 c_2 x^4-4 \log (x)-1+16 c_1}{16 x^2} \]