Internal problem ID [11273]
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]]
\[ \boxed {x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y=10 x +\frac {10}{x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 120
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)
\[ y \left (x \right ) = \frac {\left (\left (20-10 i\right ) \ln \left (x \right )+6-8 i+\left (2-i\right ) c_{1} \right ) \left (i \cos \left (\ln \left (x \right )\right )-\sin \left (\ln \left (x \right )\right )\right ) x^{-1-i}}{10}+\frac {\left (\left (20+10 i\right ) \ln \left (x \right )+6+8 i+\left (2+i\right ) c_{1} \right ) \left (-\sin \left (\ln \left (x \right )\right )-i \cos \left (\ln \left (x \right )\right )\right ) x^{-1+i}}{10}+\frac {5 x^{1-i} \left (i \sin \left (\ln \left (x \right )\right )+\cos \left (\ln \left (x \right )\right )\right )}{2}+\frac {5 \left (-i \sin \left (\ln \left (x \right )\right )+\cos \left (\ln \left (x \right )\right )\right ) x^{1+i}}{2}+x \left (\cos \left (\ln \left (x \right )\right ) c_{2} +\sin \left (\ln \left (x \right )\right ) c_{3} \right ) \]
✓ Solution by Mathematica
Time used: 0.187 (sec). Leaf size: 42
DSolve[x^3*y'''[x]+2*x^2*y''[x]+2*y[x]==10*(x+1/x),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {25 x^2+10 \log (x)+8+5 c_3}{5 x}+c_2 x \cos (\log (x))+c_1 x \sin (\log (x)) \]