62.6.3 problem Ex 3

Internal problem ID [12821]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 13. Linear equations of first order. Page 19
Problem number : Ex 3
Date solved : Tuesday, January 28, 2025 at 04:24:49 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {2 y}{1+x}&=\left (1+x \right )^{3} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

dsolve(diff(y(x),x)-2*y(x)/(1+x)=(x+1)^3,y(x), singsol=all)
 

\[ y = \left (\frac {1}{2} x^{2}+x +c_{1} \right ) \left (x +1\right )^{2} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 22

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

\[ y(x)\to (x+1)^2 \left (\frac {x^2}{2}+x+c_1\right ) \]