62.28.2 problem Ex 2

Internal problem ID [12949]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 51. Cauchy linear equation. Page 114
Problem number : Ex 2
Date solved : Tuesday, January 28, 2025 at 04:44:51 AM
CAS classification : [[_3rd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 39

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

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

✓ Solution by Mathematica

Time used: 0.187 (sec). Leaf size: 106

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

\[ y(x)\to x \sin (\log (x)) \int _1^x\frac {2 \left (K[1]^2+1\right ) (2 \cos (\log (K[1]))-\sin (\log (K[1])))}{K[1]^3}dK[1]+x \cos (\log (x)) \int _1^x-\frac {2 \left (K[2]^2+1\right ) (\cos (\log (K[2]))+2 \sin (\log (K[2])))}{K[2]^3}dK[2]+x+\frac {2 \log (x)}{x}+\frac {c_3}{x}+c_2 x \cos (\log (x))+c_1 x \sin (\log (x)) \]