Internal problem ID [2516]
Book: Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section: Exercises, page 14
Problem number: 2(n).
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 {3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 1.405 (sec). Leaf size: 5735
dsolve([(3*y(x)-7*x+7)+(7*y(x)-3*x+3)*diff(y(x),x)=0,y(0) = 0],y(x), singsol=all)
\[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 26.619 (sec). Leaf size: 546
DSolve[{(3*y[x]-7*x+7)+(7*y[x]-3*x+3)*y'[x]==0,y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{7} \left (-\frac {1}{\text {Root}\left [\text {$\#$1}^{14} \left (2560000000000 x^{14}-35840000000000 x^{13}+232960000000000 x^{12}-931840000000000 x^{11}+2562560000000000 x^{10}-5125120000000000 x^9+7687680000000000 x^8-8785920000000000 x^7+7687680000000000 x^6-5125120000000000 x^5+2562560000000000 x^4-931840000000000 x^3+232960000000000 x^2-35840000000000 x+1881776927151\right )+\text {$\#$1}^{12} \left (-448000000000 x^{12}+5376000000000 x^{11}-29568000000000 x^{10}+98560000000000 x^9-221760000000000 x^8+354816000000000 x^7-413952000000000 x^6+354816000000000 x^5-221760000000000 x^4+98560000000000 x^3-29568000000000 x^2+5376000000000 x-448000000000\right )+\text {$\#$1}^{11} \left (44800000000 x^{11}-492800000000 x^{10}+2464000000000 x^9-7392000000000 x^8+14784000000000 x^7-20697600000000 x^6+20697600000000 x^5-14784000000000 x^4+7392000000000 x^3-2464000000000 x^2+492800000000 x-44800000000\right )+\text {$\#$1}^{10} \left (28560000000 x^{10}-285600000000 x^9+1285200000000 x^8-3427200000000 x^7+5997600000000 x^6-7197120000000 x^5+5997600000000 x^4-3427200000000 x^3+1285200000000 x^2-285600000000 x+28560000000\right )+\text {$\#$1}^9 \left (-5891200000 x^9+53020800000 x^8-212083200000 x^7+494860800000 x^6-742291200000 x^5+742291200000 x^4-494860800000 x^3+212083200000 x^2-53020800000 x+5891200000\right )+\text {$\#$1}^8 \left (-453600000 x^8+3628800000 x^7-12700800000 x^6+25401600000 x^5-31752000000 x^4+25401600000 x^3-12700800000 x^2+3628800000 x-453600000\right )+\text {$\#$1}^7 \left (247680000 x^7-1733760000 x^6+5201280000 x^5-8668800000 x^4+8668800000 x^3-5201280000 x^2+1733760000 x-247680000\right )+\text {$\#$1}^6 \left (-21168000 x^6+127008000 x^5-317520000 x^4+423360000 x^3-317520000 x^2+127008000 x-21168000\right )+\text {$\#$1}^5 \left (-1993600 x^5+9968000 x^4-19936000 x^3+19936000 x^2-9968000 x+1993600\right )+\text {$\#$1}^4 \left (586656 x^4-2346624 x^3+3519936 x^2-2346624 x+586656\right )+\text {$\#$1}^3 \left (-57344 x^3+172032 x^2-172032 x+57344\right )+\text {$\#$1}^2 \left (2996 x^2-5992 x+2996\right )+\text {$\#$1} (84-84 x)+1\&,1\right ]}+3 x-3\right ) \\ \end{align*}