Internal problem ID [4181]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 32
Problem number: 947.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, _dAlembert]
\[ \boxed {y {y^{\prime }}^{2}-\left (-2 b x +a \right ) y^{\prime }-y b=0} \]
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 201
dsolve(y(x)*diff(y(x),x)^2-(-2*b*x+a)*diff(y(x),x)-b*y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {-2 x b +a}{2 \sqrt {-b}} y \left (x \right ) = \frac {-2 x b +a}{2 \sqrt {-b}} y \left (x \right ) = 0 y \left (x \right ) = \sqrt {\frac {c_{1} b +\sqrt {4 b^{3} c_{1} x^{2}-4 a \,b^{2} c_{1} x +a^{2} b c_{1}}}{b}} y \left (x \right ) = \sqrt {\frac {c_{1} b -\sqrt {4 b^{3} c_{1} x^{2}-4 a \,b^{2} c_{1} x +a^{2} b c_{1}}}{b}} y \left (x \right ) = -\sqrt {\frac {c_{1} b +\sqrt {4 b^{3} c_{1} x^{2}-4 a \,b^{2} c_{1} x +a^{2} b c_{1}}}{b}} y \left (x \right ) = -\sqrt {\frac {c_{1} b -\sqrt {4 b^{3} c_{1} x^{2}-4 a \,b^{2} c_{1} x +a^{2} b c_{1}}}{b}} \end{align*}
✓ Solution by Mathematica
Time used: 1.067 (sec). Leaf size: 409
DSolve[y[x] (y'[x])^2-(a-2 b x)y'[x]-b y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [\frac {\left (b-\sqrt {b^2}\right ) \log (y(x))}{b}-\frac {-b \log \left (\sqrt {a^2-4 a b x+4 b \left (b x^2+y(x)^2\right )}-a-2 \sqrt {b^2} x\right )+\sqrt {b^2} \log \left (b \left (\sqrt {a^2-4 a b x+4 b \left (b x^2+y(x)^2\right )}-a-2 \sqrt {b^2} x\right )\right )-\left (\sqrt {b^2}+b\right ) \log \left (\sqrt {a^2-4 a b x+4 b \left (b x^2+y(x)^2\right )}+a-2 \sqrt {b^2} x\right )}{2 \sqrt {b^2}}=c_1,y(x)\right ] \text {Solve}\left [\frac {-b \log \left (\sqrt {a^2-4 a b x+4 b \left (b x^2+y(x)^2\right )}-a-2 \sqrt {b^2} x\right )+\sqrt {b^2} \log \left (b \left (\sqrt {a^2-4 a b x+4 b \left (b x^2+y(x)^2\right )}-a-2 \sqrt {b^2} x\right )\right )-\left (\sqrt {b^2}+b\right ) \log \left (\sqrt {a^2-4 a b x+4 b \left (b x^2+y(x)^2\right )}+a-2 \sqrt {b^2} x\right )}{2 \sqrt {b^2}}+\frac {\left (\sqrt {b^2}+b\right ) \log (y(x))}{b}=c_1,y(x)\right ] y(x)\to -\frac {i (2 b x-a)}{2 \sqrt {b}} y(x)\to \frac {i (2 b x-a)}{2 \sqrt {b}} \end{align*}