Internal problem ID [2515]
Book: Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section: Exercises, page 14
Problem number: 2(m).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {3 x -y+1}{3 y-x +5}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 5.203 (sec). Leaf size: 84
dsolve([diff(y(x),x)=(3*x-y(x)+1)/(3*y(x)-x+5),y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{\frac {4}{3}}-12 \left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{\frac {2}{3}} x -84 \left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{\frac {2}{3}}+576 x^{2}+1152 x +576}{36 \left (-324+12 \sqrt {96 x^{3}+288 x^{2}+288 x +825}\right )^{\frac {2}{3}}} \]
✓ Solution by Mathematica
Time used: 60.735 (sec). Leaf size: 341
DSolve[{y'[x]==(3*x-y[x]+1)/(3*y[x]-x+5),y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+6144 x^5+15360 x^4+20480 x^3+15360 x^2+6144 x-58025\right )+\text {$\#$1}^4 \left (-384 x^4-1536 x^3-2304 x^2-1536 x-384\right )+\text {$\#$1}^3 \left (64 x^3+192 x^2+192 x+64\right )+\text {$\#$1}^2 \left (36 x^2+72 x+36\right )+\text {$\#$1} (-12 x-12)+1\&,1\right ]-5 \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+6144 x^5+15360 x^4+20480 x^3+15360 x^2+6144 x-58025\right )+\text {$\#$1}^4 \left (-384 x^4-1536 x^3-2304 x^2-1536 x-384\right )+\text {$\#$1}^3 \left (64 x^3+192 x^2+192 x+64\right )+\text {$\#$1}^2 \left (36 x^2+72 x+36\right )+\text {$\#$1} (-12 x-12)+1\&,1\right ]-1}{3 \text {Root}\left [\text {$\#$1}^6 \left (1024 x^6+6144 x^5+15360 x^4+20480 x^3+15360 x^2+6144 x-58025\right )+\text {$\#$1}^4 \left (-384 x^4-1536 x^3-2304 x^2-1536 x-384\right )+\text {$\#$1}^3 \left (64 x^3+192 x^2+192 x+64\right )+\text {$\#$1}^2 \left (36 x^2+72 x+36\right )+\text {$\#$1} (-12 x-12)+1\&,1\right ]} \\ \end{align*}