62.36.1 problem Ex 1

Internal problem ID [12999]
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
Date solved : Tuesday, January 28, 2025 at 04:47:11 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} \left (x +2\right )^{2} y^{\prime \prime \prime }+\left (x +2\right ) y^{\prime \prime }+y^{\prime }&=1 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 35

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)
 

\[ y = \frac {\left (c_{1} -c_{2} \right ) \left (x +2\right ) \cos \left (\ln \left (x +2\right )\right )}{2}+\frac {\left (c_{1} +c_{2} \right ) \left (x +2\right ) \sin \left (\ln \left (x +2\right )\right )}{2}+x +c_{3} \]

✓ Solution by Mathematica

Time used: 60.028 (sec). Leaf size: 35

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

\[ y(x)\to \int _1^x(c_1 \cos (\log (K[1]+2))+c_2 \sin (\log (K[1]+2))+1)dK[1]+c_3 \]