82.39.6 problem Ex. 6

Internal problem ID [18938]
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. 6
Date solved : Tuesday, January 28, 2025 at 12:37:29 PM
CAS classification : [[_3rd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y&=10 c +\frac {10}{x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 38

dsolve(x^3*diff(y(x),x$3)+2*x^2*diff(y(x),x$2)+2*y(x)=10*(c+1/x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {5 x^{2} \sin \left (\ln \left (x \right )\right ) c_3 +5 x^{2} \cos \left (\ln \left (x \right )\right ) c_{2} +25 c x +10 \ln \left (x \right )+c_{1} +8}{5 x} \]

✓ Solution by Mathematica

Time used: 0.116 (sec). Leaf size: 43

DSolve[x^3*D[y[x],{x,3}]+2*x^2*D[y[x],{x,2}]+2*y[x]==10*(c+1/x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 5 c+\frac {8}{5 x}+\frac {2 \log (x)}{x}+\frac {c_3}{x}+c_2 x \cos (\log (x))+c_1 x \sin (\log (x)) \]