Internal problem ID [4524]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12,
Miscellaneous Methods
Problem number: Exercise 12.3, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {\left (x +1\right ) y^{\prime }-y-\left (x +1\right ) \sqrt {1+y}=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 81
dsolve((x+1)*diff(y(x),x)-(y(x)+1)=(x+1)*sqrt(y(x)+1),y(x), singsol=all)
\[ \frac {\left (-c_{1} y \left (x \right )+1+c_{1} x^{2}+\left (2 c_{1} +1\right ) x \right ) \sqrt {y \left (x \right )+1}-\left (1+x \right ) \left (-c_{1} y \left (x \right )-1+c_{1} x^{2}+\left (2 c_{1} -1\right ) x \right )}{\left (x^{2}+2 x -y \left (x \right )\right ) \left (-\sqrt {y \left (x \right )+1}+1+x \right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.244 (sec). Leaf size: 60
DSolve[(x+1)*y'[x]-(y[x]+1)==(x+1)*Sqrt[y[x]+1],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2 \sqrt {y(x)+1} \arctan \left (\frac {x+1}{\sqrt {-y(x)-1}}\right )}{\sqrt {-y(x)-1}}+\log \left (y(x)-(x+1)^2+1\right )-\log (x+1)=c_1,y(x)\right ] \]