Internal problem ID [3392]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 5
Problem number: 135.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {y^{\prime }-f \left (a +b x +c y\right )=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 39
dsolve(diff(y(x),x) = f(a+b*x+c*y(x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (\left (\int _{}^{\textit {\_Z}}\frac {1}{f \left (\textit {\_a} c +a \right ) c +b}d \textit {\_a} \right ) c -x +c_{1} \right ) c -b x}{c} \]
✓ Solution by Mathematica
Time used: 0.225 (sec). Leaf size: 262
DSolve[y'[x]==f[a+b x +c y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}-\frac {f(a+b x+c K[2]) \int _1^x\left (\frac {c^2 f'(a+b K[1]+c K[2])}{b+c f(a+b K[1]+c K[2])}-\frac {c^3 f(a+b K[1]+c K[2]) f'(a+b K[1]+c K[2])}{(b+c f(a+b K[1]+c K[2]))^2}\right )dK[1] c+c+b \int _1^x\left (\frac {c^2 f'(a+b K[1]+c K[2])}{b+c f(a+b K[1]+c K[2])}-\frac {c^3 f(a+b K[1]+c K[2]) f'(a+b K[1]+c K[2])}{(b+c f(a+b K[1]+c K[2]))^2}\right )dK[1]}{b+c f(a+b x+c K[2])}dK[2]+\int _1^x\frac {c f(a+b K[1]+c y(x))}{b+c f(a+b K[1]+c y(x))}dK[1]=c_1,y(x)\right ] \]