82.39.11 problem Ex. 11

Internal problem ID [18943]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VII. Linear equations with variable coefficients. End of chapter problems at page 91
Problem number : Ex. 11
Date solved : Tuesday, January 28, 2025 at 12:37:36 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 30

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

\[ y \left (x \right ) = \frac {4 c_3 \,x^{2} \ln \left (x \right )+4 c_{1} x^{2}+\ln \left (x \right )+4 c_{2} +1}{4 x} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 33

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

\[ y(x)\to \frac {\log (x)+1}{4 x}+\frac {c_1}{x}+c_2 x+c_3 x \log (x) \]