60.1.63 problem 63

Internal problem ID [10077]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 63
Date solved : Monday, January 27, 2025 at 06:23:05 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }-\frac {1+y^{2}}{{| y+\sqrt {y+1}|} \left (1+x \right )^{{3}/{2}}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 35

dsolve(diff(y(x),x) - (1+ y(x)^2)/(abs(y(x)+sqrt(1+y(x)))*sqrt(1+x)^3)=0,y(x), singsol=all)
 

\[ -\frac {2}{\sqrt {x +1}}-\int _{}^{y}\frac {{| \textit {\_a} +\sqrt {\textit {\_a} +1}|}}{\textit {\_a}^{2}+1}d \textit {\_a} +c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.379 (sec). Leaf size: 62

DSolve[D[y[x],x] - (1+ y[x]^2)/(Abs[y[x]+Sqrt[1+y[x]]]*Sqrt[1+x]^3)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\left | K[1]+\sqrt {K[1]+1}\right | }{K[1]^2+1}dK[1]\&\right ]\left [-\frac {2}{\sqrt {x+1}}+c_1\right ] \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}