Internal problem ID [10255]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y-10 x -\frac {10}{x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 146
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)
\[ y \left (x \right ) = \sin \left (\ln \left (x \right )\right ) x c_{3} +\cos \left (\ln \left (x \right )\right ) x c_{2} +\frac {\left (\left (\left (10+20 i\right ) \ln \left (x \right )+8+6 i+\left (1+2 i\right ) c_{1} \right ) \cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right ) \left (\left (-20+10 i\right ) \ln \left (x \right )-6+8 i+\left (-2+i\right ) c_{1} \right )\right ) x^{-1-i}}{10}+\frac {\left (\left (\left (10-20 i\right ) \ln \left (x \right )+8-6 i+\left (1-2 i\right ) c_{1} \right ) \cos \left (\ln \left (x \right )\right )-\sin \left (\ln \left (x \right )\right ) \left (\left (20+10 i\right ) \ln \left (x \right )+6+8 i+\left (2+i\right ) c_{1} \right )\right ) x^{-1+i}}{10}+\frac {5 \left (i \sin \left (\ln \left (x \right )\right )+\cos \left (\ln \left (x \right )\right )\right ) x^{1-i}}{2}-\frac {5 x^{1+i} \left (i \sin \left (\ln \left (x \right )\right )-\cos \left (\ln \left (x \right )\right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.118 (sec). Leaf size: 40
DSolve[x^3*y'''[x]+2*x^2*y''[x]+2*y[x]==10*(x+1/x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 5 x+\frac {2 \log (x)}{x}+\frac {\frac {8}{5}+c_3}{x}+c_2 x \cos (\log (x))+c_1 x \sin (\log (x)) \\ \end{align*}