Internal problem ID [1939]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 7, page 28
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {2 y-\left (x +2 y-1\right ) y^{\prime }=-3 x -3} \] With initial conditions \begin {align*} [y \left (-2\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 1.282 (sec). Leaf size: 136
dsolve([(3*x+2*y(x)+3)-(x+2*y(x)-1)*diff(y(x),x)=0,y(-2) = 1],y(x), singsol=all)
\[ y = \frac {\left (-x -2\right ) {\operatorname {RootOf}\left (-1+\left (x^{5}+10 x^{4}+40 x^{3}+80 x^{2}+80 x +32\right ) \textit {\_Z}^{25}+\left (-5 x^{5}-50 x^{4}-200 x^{3}-400 x^{2}-400 x -160\right ) \textit {\_Z}^{20}\right )}^{5}}{2}+\frac {3 x}{2}+\frac {9}{2} \]
✓ Solution by Mathematica
Time used: 63.287 (sec). Leaf size: 850
DSolve[{(3*x+2*y[x]+3)-(x+2*y[x]-1)*y'[x]==0,{y[-2]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-x \text {Root}\left [\left (65536 x^{10}+1310720 x^9+11796480 x^8+62914560 x^7+220200960 x^6+528482304 x^5+880803840 x^4+1006632960 x^3+754974720 x^2+335544320 x+67108863\right ) \text {$\#$1}^{10}+\left (-81920 x^8-1310720 x^7-9175040 x^6-36700160 x^5-91750400 x^4-146800640 x^3-146800640 x^2-83886080 x-20971520\right ) \text {$\#$1}^8+\left (40960 x^7+573440 x^6+3440640 x^5+11468800 x^4+22937600 x^3+27525120 x^2+18350080 x+5242880\right ) \text {$\#$1}^7+\left (17920 x^6+215040 x^5+1075200 x^4+2867200 x^3+4300800 x^2+3440640 x+1146880\right ) \text {$\#$1}^6+\left (-25088 x^5-250880 x^4-1003520 x^3-2007040 x^2-2007040 x-802816\right ) \text {$\#$1}^5+\left (11200 x^4+89600 x^3+268800 x^2+358400 x+179200\right ) \text {$\#$1}^4+\left (-2720 x^3-16320 x^2-32640 x-21760\right ) \text {$\#$1}^3+\left (385 x^2+1540 x+1540\right ) \text {$\#$1}^2+(-30 x-60) \text {$\#$1}+1\&,1\right ]+\text {Root}\left [\left (65536 x^{10}+1310720 x^9+11796480 x^8+62914560 x^7+220200960 x^6+528482304 x^5+880803840 x^4+1006632960 x^3+754974720 x^2+335544320 x+67108863\right ) \text {$\#$1}^{10}+\left (-81920 x^8-1310720 x^7-9175040 x^6-36700160 x^5-91750400 x^4-146800640 x^3-146800640 x^2-83886080 x-20971520\right ) \text {$\#$1}^8+\left (40960 x^7+573440 x^6+3440640 x^5+11468800 x^4+22937600 x^3+27525120 x^2+18350080 x+5242880\right ) \text {$\#$1}^7+\left (17920 x^6+215040 x^5+1075200 x^4+2867200 x^3+4300800 x^2+3440640 x+1146880\right ) \text {$\#$1}^6+\left (-25088 x^5-250880 x^4-1003520 x^3-2007040 x^2-2007040 x-802816\right ) \text {$\#$1}^5+\left (11200 x^4+89600 x^3+268800 x^2+358400 x+179200\right ) \text {$\#$1}^4+\left (-2720 x^3-16320 x^2-32640 x-21760\right ) \text {$\#$1}^3+\left (385 x^2+1540 x+1540\right ) \text {$\#$1}^2+(-30 x-60) \text {$\#$1}+1\&,1\right ]+1}{2 \text {Root}\left [\left (65536 x^{10}+1310720 x^9+11796480 x^8+62914560 x^7+220200960 x^6+528482304 x^5+880803840 x^4+1006632960 x^3+754974720 x^2+335544320 x+67108863\right ) \text {$\#$1}^{10}+\left (-81920 x^8-1310720 x^7-9175040 x^6-36700160 x^5-91750400 x^4-146800640 x^3-146800640 x^2-83886080 x-20971520\right ) \text {$\#$1}^8+\left (40960 x^7+573440 x^6+3440640 x^5+11468800 x^4+22937600 x^3+27525120 x^2+18350080 x+5242880\right ) \text {$\#$1}^7+\left (17920 x^6+215040 x^5+1075200 x^4+2867200 x^3+4300800 x^2+3440640 x+1146880\right ) \text {$\#$1}^6+\left (-25088 x^5-250880 x^4-1003520 x^3-2007040 x^2-2007040 x-802816\right ) \text {$\#$1}^5+\left (11200 x^4+89600 x^3+268800 x^2+358400 x+179200\right ) \text {$\#$1}^4+\left (-2720 x^3-16320 x^2-32640 x-21760\right ) \text {$\#$1}^3+\left (385 x^2+1540 x+1540\right ) \text {$\#$1}^2+(-30 x-60) \text {$\#$1}+1\&,1\right ]} \]