Internal problem ID [3483]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 227.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {\left (x +1\right ) y^{\prime }-y-\left (x +1\right ) \sqrt {y+1}=1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 81
dsolve((1+x)*diff(y(x),x) = 1+y(x)+(1+x)*sqrt(1+y(x)),y(x), singsol=all)
\[ \frac {\left (-c_{1} y \left (x \right )+1+c_{1} x^{2}+\left (2 c_{1} +1\right ) x \right ) \sqrt {y \left (x \right )+1}-\left (-c_{1} y \left (x \right )-1+c_{1} x^{2}+\left (2 c_{1} -1\right ) x \right ) \left (x +1\right )}{\left (x^{2}+2 x -y \left (x \right )\right ) \left (-\sqrt {y \left (x \right )+1}+x +1\right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.237 (sec). Leaf size: 60
DSolve[(1+x) y'[x]==(1+y[x])+(1+x)Sqrt[1+y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {2 \sqrt {y(x)+1} \arctan \left (\frac {x+1}{\sqrt {-y(x)-1}}\right )}{\sqrt {-y(x)-1}}+\log \left (y(x)-(x+1)^2+1\right )-\log (x+1)=c_1,y(x)\right ] \]