40.3.28 problem 26 (b)

Internal problem ID [6632]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 26 (b)
Date solved : Monday, January 27, 2025 at 02:16:22 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 15

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

\[ y = \tan \left (-\ln \left (x +1\right )+\ln \left (x \right )+c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.300 (sec). Leaf size: 31

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

\begin{align*} y(x)\to \tan (\log (x)-\log (x+1)+c_1) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}