Internal problem ID [10305]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 60.
Exact equation. Integrating factor. Page 139
Problem number: Ex 1.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {\left (x +2\right )^{2} y^{\prime \prime \prime }+\left (x +2\right ) y^{\prime \prime }+y^{\prime }-1=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 53
dsolve((x+2)^2*diff(y(x),x$3)+(x+2)*diff(y(x),x$2)+diff(y(x),x)=1,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \left (\frac {\cos \left (\ln \left (x +2\right )\right ) \left (x +2\right )}{2}+\frac {\left (x +2\right ) \sin \left (\ln \left (x +2\right )\right )}{2}\right )+c_{2} \left (-\frac {\cos \left (\ln \left (x +2\right )\right ) \left (x +2\right )}{2}+\frac {\left (x +2\right ) \sin \left (\ln \left (x +2\right )\right )}{2}\right )+x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 41
DSolve[(x+2)^2*y'''[x]+(x+2)*y''[x]+y'[x]==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\frac {1}{2} (x+2) ((c_1-c_2) \cos (\log (x+2))+(c_1+c_2) \sin (\log (x+2)))+c_3 \\ \end{align*}