56.3.16 problem 16

Internal problem ID [8874]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 16
Date solved : Monday, January 27, 2025 at 05:11:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 22

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

\[ y = \frac {3 c_{2} x^{4}+3 c_{1} -x}{3 x^{2}} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 25

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

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