Internal problem ID [10309]
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]]
Solve \begin {gather*} \boxed {\left (x +2\right )^{2} y^{\prime \prime \prime }+\left (x +2\right ) y^{\prime \prime }+y^{\prime }-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 117
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)
\[ y \relax (x ) = \frac {c_{1} x \tan \left (\frac {\ln \left (x +2\right )}{2}\right )+\frac {x c_{1}}{2}+2 c_{1} \tan \left (\frac {\ln \left (x +2\right )}{2}\right )-\frac {c_{1} x \left (\tan ^{2}\left (\frac {\ln \left (x +2\right )}{2}\right )\right )}{2}+2 c_{1}}{1+\tan ^{2}\left (\frac {\ln \left (x +2\right )}{2}\right )}+\frac {c_{2} x \tan \left (\frac {\ln \left (x +2\right )}{2}\right )-\frac {c_{2} x}{2}+2 c_{2} \tan \left (\frac {\ln \left (x +2\right )}{2}\right )+\frac {c_{2} x \left (\tan ^{2}\left (\frac {\ln \left (x +2\right )}{2}\right )\right )}{2}-2 c_{2}}{1+\tan ^{2}\left (\frac {\ln \left (x +2\right )}{2}\right )}+x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.033 (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*}