Internal problem ID [3358]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 4
Problem number: 100.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _Chini]
\[ \boxed {y^{\prime }-b \sqrt {y}=a x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 68
dsolve(diff(y(x),x) = a*x+b*sqrt(y(x)),y(x), singsol=all)
\[ -\frac {\ln \left (\sqrt {y \left (x \right )}\, b x +a \,x^{2}-2 y \left (x \right )\right )}{2}+\frac {b \sqrt {y \left (x \right )}\, \operatorname {arctanh}\left (\frac {b \sqrt {y \left (x \right )}+2 a x}{\sqrt {y \left (x \right ) \left (b^{2}+8 a \right )}}\right )}{\sqrt {y \left (x \right ) \left (b^{2}+8 a \right )}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.267 (sec). Leaf size: 119
DSolve[y'[x]==a x+b Sqrt[y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {b^2 \left (-\frac {2 b \text {arctanh}\left (\frac {b^2-4 a \sqrt {\frac {b^2 y(x)}{a^2 x^2}}}{b \sqrt {8 a+b^2}}\right )}{\sqrt {8 a+b^2}}-\log \left (b^2 \left (\sqrt {\frac {b^2 y(x)}{a^2 x^2}}+1\right )-\frac {2 b^2 y(x)}{a x^2}\right )\right )}{2 a}=\frac {b^2 \log (x)}{a}+c_1,y(x)\right ] \]