4.10.4 \((y(x)-3 x+1) y'(x)=2 (x-y(x))\)

ODE
\[ (y(x)-3 x+1) y'(x)=2 (x-y(x)) \] ODE Classification

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Book solution method
Equation linear in the variables, \(y'(x)=f\left ( \frac {X_1}{X_2} \right ) \)

Mathematica ✓
cpu = 0.35677 (sec), leaf count = 4937

\[\left \{\left \{y(x)\to 3 x-\frac {1}{\text {Root}\left [\left (65536 e^{\frac {24 c_1}{25}} x^8-262144 e^{\frac {24 c_1}{25}} x^7+458752 e^{\frac {24 c_1}{25}} x^6-458752 e^{\frac {24 c_1}{25}} x^5+286720 e^{\frac {24 c_1}{25}} x^4-114688 e^{\frac {24 c_1}{25}} x^3+28672 e^{\frac {24 c_1}{25}} x^2+16 x^2-4096 e^{\frac {24 c_1}{25}} x-16 x+256 e^{\frac {24 c_1}{25}}+4\right ) \text {$\#$1}^8+\left (-131072 e^{\frac {24 c_1}{25}} x^7+458752 e^{\frac {24 c_1}{25}} x^6-688128 e^{\frac {24 c_1}{25}} x^5+573440 e^{\frac {24 c_1}{25}} x^4-286720 e^{\frac {24 c_1}{25}} x^3+86016 e^{\frac {24 c_1}{25}} x^2-14336 e^{\frac {24 c_1}{25}} x-32 x+1024 e^{\frac {24 c_1}{25}}+16\right ) \text {$\#$1}^7+\left (114688 e^{\frac {24 c_1}{25}} x^6-344064 e^{\frac {24 c_1}{25}} x^5+430080 e^{\frac {24 c_1}{25}} x^4-286720 e^{\frac {24 c_1}{25}} x^3+107520 e^{\frac {24 c_1}{25}} x^2-21504 e^{\frac {24 c_1}{25}} x+1792 e^{\frac {24 c_1}{25}}+16\right ) \text {$\#$1}^6+\left (-57344 e^{\frac {24 c_1}{25}} x^5+143360 e^{\frac {24 c_1}{25}} x^4-143360 e^{\frac {24 c_1}{25}} x^3+71680 e^{\frac {24 c_1}{25}} x^2-17920 e^{\frac {24 c_1}{25}} x+1792 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^5+\left (17920 e^{\frac {24 c_1}{25}} x^4-35840 e^{\frac {24 c_1}{25}} x^3+26880 e^{\frac {24 c_1}{25}} x^2-8960 e^{\frac {24 c_1}{25}} x+1120 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^4+\left (-3584 e^{\frac {24 c_1}{25}} x^3+5376 e^{\frac {24 c_1}{25}} x^2-2688 e^{\frac {24 c_1}{25}} x+448 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^3+\left (448 e^{\frac {24 c_1}{25}} x^2-448 e^{\frac {24 c_1}{25}} x+112 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^2+\left (16 e^{\frac {24 c_1}{25}}-32 e^{\frac {24 c_1}{25}} x\right ) \text {$\#$1}+e^{\frac {24 c_1}{25}}\& ,1\right ]}-1\right \},\left \{y(x)\to 3 x-\frac {1}{\text {Root}\left [\left (65536 e^{\frac {24 c_1}{25}} x^8-262144 e^{\frac {24 c_1}{25}} x^7+458752 e^{\frac {24 c_1}{25}} x^6-458752 e^{\frac {24 c_1}{25}} x^5+286720 e^{\frac {24 c_1}{25}} x^4-114688 e^{\frac {24 c_1}{25}} x^3+28672 e^{\frac {24 c_1}{25}} x^2+16 x^2-4096 e^{\frac {24 c_1}{25}} x-16 x+256 e^{\frac {24 c_1}{25}}+4\right ) \text {$\#$1}^8+\left (-131072 e^{\frac {24 c_1}{25}} x^7+458752 e^{\frac {24 c_1}{25}} x^6-688128 e^{\frac {24 c_1}{25}} x^5+573440 e^{\frac {24 c_1}{25}} x^4-286720 e^{\frac {24 c_1}{25}} x^3+86016 e^{\frac {24 c_1}{25}} x^2-14336 e^{\frac {24 c_1}{25}} x-32 x+1024 e^{\frac {24 c_1}{25}}+16\right ) \text {$\#$1}^7+\left (114688 e^{\frac {24 c_1}{25}} x^6-344064 e^{\frac {24 c_1}{25}} x^5+430080 e^{\frac {24 c_1}{25}} x^4-286720 e^{\frac {24 c_1}{25}} x^3+107520 e^{\frac {24 c_1}{25}} x^2-21504 e^{\frac {24 c_1}{25}} x+1792 e^{\frac {24 c_1}{25}}+16\right ) \text {$\#$1}^6+\left (-57344 e^{\frac {24 c_1}{25}} x^5+143360 e^{\frac {24 c_1}{25}} x^4-143360 e^{\frac {24 c_1}{25}} x^3+71680 e^{\frac {24 c_1}{25}} x^2-17920 e^{\frac {24 c_1}{25}} x+1792 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^5+\left (17920 e^{\frac {24 c_1}{25}} x^4-35840 e^{\frac {24 c_1}{25}} x^3+26880 e^{\frac {24 c_1}{25}} x^2-8960 e^{\frac {24 c_1}{25}} x+1120 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^4+\left (-3584 e^{\frac {24 c_1}{25}} x^3+5376 e^{\frac {24 c_1}{25}} x^2-2688 e^{\frac {24 c_1}{25}} x+448 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^3+\left (448 e^{\frac {24 c_1}{25}} x^2-448 e^{\frac {24 c_1}{25}} x+112 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^2+\left (16 e^{\frac {24 c_1}{25}}-32 e^{\frac {24 c_1}{25}} x\right ) \text {$\#$1}+e^{\frac {24 c_1}{25}}\& ,2\right ]}-1\right \},\left \{y(x)\to 3 x-\frac {1}{\text {Root}\left [\left (65536 e^{\frac {24 c_1}{25}} x^8-262144 e^{\frac {24 c_1}{25}} x^7+458752 e^{\frac {24 c_1}{25}} x^6-458752 e^{\frac {24 c_1}{25}} x^5+286720 e^{\frac {24 c_1}{25}} x^4-114688 e^{\frac {24 c_1}{25}} x^3+28672 e^{\frac {24 c_1}{25}} x^2+16 x^2-4096 e^{\frac {24 c_1}{25}} x-16 x+256 e^{\frac {24 c_1}{25}}+4\right ) \text {$\#$1}^8+\left (-131072 e^{\frac {24 c_1}{25}} x^7+458752 e^{\frac {24 c_1}{25}} x^6-688128 e^{\frac {24 c_1}{25}} x^5+573440 e^{\frac {24 c_1}{25}} x^4-286720 e^{\frac {24 c_1}{25}} x^3+86016 e^{\frac {24 c_1}{25}} x^2-14336 e^{\frac {24 c_1}{25}} x-32 x+1024 e^{\frac {24 c_1}{25}}+16\right ) \text {$\#$1}^7+\left (114688 e^{\frac {24 c_1}{25}} x^6-344064 e^{\frac {24 c_1}{25}} x^5+430080 e^{\frac {24 c_1}{25}} x^4-286720 e^{\frac {24 c_1}{25}} x^3+107520 e^{\frac {24 c_1}{25}} x^2-21504 e^{\frac {24 c_1}{25}} x+1792 e^{\frac {24 c_1}{25}}+16\right ) \text {$\#$1}^6+\left (-57344 e^{\frac {24 c_1}{25}} x^5+143360 e^{\frac {24 c_1}{25}} x^4-143360 e^{\frac {24 c_1}{25}} x^3+71680 e^{\frac {24 c_1}{25}} x^2-17920 e^{\frac {24 c_1}{25}} x+1792 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^5+\left (17920 e^{\frac {24 c_1}{25}} x^4-35840 e^{\frac {24 c_1}{25}} x^3+26880 e^{\frac {24 c_1}{25}} x^2-8960 e^{\frac {24 c_1}{25}} x+1120 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^4+\left (-3584 e^{\frac {24 c_1}{25}} x^3+5376 e^{\frac {24 c_1}{25}} x^2-2688 e^{\frac {24 c_1}{25}} x+448 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^3+\left (448 e^{\frac {24 c_1}{25}} x^2-448 e^{\frac {24 c_1}{25}} x+112 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^2+\left (16 e^{\frac {24 c_1}{25}}-32 e^{\frac {24 c_1}{25}} x\right ) \text {$\#$1}+e^{\frac {24 c_1}{25}}\& ,3\right ]}-1\right \},\left \{y(x)\to 3 x-\frac {1}{\text {Root}\left [\left (65536 e^{\frac {24 c_1}{25}} x^8-262144 e^{\frac {24 c_1}{25}} x^7+458752 e^{\frac {24 c_1}{25}} x^6-458752 e^{\frac {24 c_1}{25}} x^5+286720 e^{\frac {24 c_1}{25}} x^4-114688 e^{\frac {24 c_1}{25}} x^3+28672 e^{\frac {24 c_1}{25}} x^2+16 x^2-4096 e^{\frac {24 c_1}{25}} x-16 x+256 e^{\frac {24 c_1}{25}}+4\right ) \text {$\#$1}^8+\left (-131072 e^{\frac {24 c_1}{25}} x^7+458752 e^{\frac {24 c_1}{25}} x^6-688128 e^{\frac {24 c_1}{25}} x^5+573440 e^{\frac {24 c_1}{25}} x^4-286720 e^{\frac {24 c_1}{25}} x^3+86016 e^{\frac {24 c_1}{25}} x^2-14336 e^{\frac {24 c_1}{25}} x-32 x+1024 e^{\frac {24 c_1}{25}}+16\right ) \text {$\#$1}^7+\left (114688 e^{\frac {24 c_1}{25}} x^6-344064 e^{\frac {24 c_1}{25}} x^5+430080 e^{\frac {24 c_1}{25}} x^4-286720 e^{\frac {24 c_1}{25}} x^3+107520 e^{\frac {24 c_1}{25}} x^2-21504 e^{\frac {24 c_1}{25}} x+1792 e^{\frac {24 c_1}{25}}+16\right ) \text {$\#$1}^6+\left (-57344 e^{\frac {24 c_1}{25}} x^5+143360 e^{\frac {24 c_1}{25}} x^4-143360 e^{\frac {24 c_1}{25}} x^3+71680 e^{\frac {24 c_1}{25}} x^2-17920 e^{\frac {24 c_1}{25}} x+1792 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^5+\left (17920 e^{\frac {24 c_1}{25}} x^4-35840 e^{\frac {24 c_1}{25}} x^3+26880 e^{\frac {24 c_1}{25}} x^2-8960 e^{\frac {24 c_1}{25}} x+1120 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^4+\left (-3584 e^{\frac {24 c_1}{25}} x^3+5376 e^{\frac {24 c_1}{25}} x^2-2688 e^{\frac {24 c_1}{25}} x+448 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^3+\left (448 e^{\frac {24 c_1}{25}} x^2-448 e^{\frac {24 c_1}{25}} x+112 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^2+\left (16 e^{\frac {24 c_1}{25}}-32 e^{\frac {24 c_1}{25}} x\right ) \text {$\#$1}+e^{\frac {24 c_1}{25}}\& ,4\right ]}-1\right \},\left \{y(x)\to 3 x-\frac {1}{\text {Root}\left [\left (65536 e^{\frac {24 c_1}{25}} x^8-262144 e^{\frac {24 c_1}{25}} x^7+458752 e^{\frac {24 c_1}{25}} x^6-458752 e^{\frac {24 c_1}{25}} x^5+286720 e^{\frac {24 c_1}{25}} x^4-114688 e^{\frac {24 c_1}{25}} x^3+28672 e^{\frac {24 c_1}{25}} x^2+16 x^2-4096 e^{\frac {24 c_1}{25}} x-16 x+256 e^{\frac {24 c_1}{25}}+4\right ) \text {$\#$1}^8+\left (-131072 e^{\frac {24 c_1}{25}} x^7+458752 e^{\frac {24 c_1}{25}} x^6-688128 e^{\frac {24 c_1}{25}} x^5+573440 e^{\frac {24 c_1}{25}} x^4-286720 e^{\frac {24 c_1}{25}} x^3+86016 e^{\frac {24 c_1}{25}} x^2-14336 e^{\frac {24 c_1}{25}} x-32 x+1024 e^{\frac {24 c_1}{25}}+16\right ) \text {$\#$1}^7+\left (114688 e^{\frac {24 c_1}{25}} x^6-344064 e^{\frac {24 c_1}{25}} x^5+430080 e^{\frac {24 c_1}{25}} x^4-286720 e^{\frac {24 c_1}{25}} x^3+107520 e^{\frac {24 c_1}{25}} x^2-21504 e^{\frac {24 c_1}{25}} x+1792 e^{\frac {24 c_1}{25}}+16\right ) \text {$\#$1}^6+\left (-57344 e^{\frac {24 c_1}{25}} x^5+143360 e^{\frac {24 c_1}{25}} x^4-143360 e^{\frac {24 c_1}{25}} x^3+71680 e^{\frac {24 c_1}{25}} x^2-17920 e^{\frac {24 c_1}{25}} x+1792 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^5+\left (17920 e^{\frac {24 c_1}{25}} x^4-35840 e^{\frac {24 c_1}{25}} x^3+26880 e^{\frac {24 c_1}{25}} x^2-8960 e^{\frac {24 c_1}{25}} x+1120 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^4+\left (-3584 e^{\frac {24 c_1}{25}} x^3+5376 e^{\frac {24 c_1}{25}} x^2-2688 e^{\frac {24 c_1}{25}} x+448 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^3+\left (448 e^{\frac {24 c_1}{25}} x^2-448 e^{\frac {24 c_1}{25}} x+112 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^2+\left (16 e^{\frac {24 c_1}{25}}-32 e^{\frac {24 c_1}{25}} x\right ) \text {$\#$1}+e^{\frac {24 c_1}{25}}\& ,5\right ]}-1\right \},\left \{y(x)\to 3 x-\frac {1}{\text {Root}\left [\left (65536 e^{\frac {24 c_1}{25}} x^8-262144 e^{\frac {24 c_1}{25}} x^7+458752 e^{\frac {24 c_1}{25}} x^6-458752 e^{\frac {24 c_1}{25}} x^5+286720 e^{\frac {24 c_1}{25}} x^4-114688 e^{\frac {24 c_1}{25}} x^3+28672 e^{\frac {24 c_1}{25}} x^2+16 x^2-4096 e^{\frac {24 c_1}{25}} x-16 x+256 e^{\frac {24 c_1}{25}}+4\right ) \text {$\#$1}^8+\left (-131072 e^{\frac {24 c_1}{25}} x^7+458752 e^{\frac {24 c_1}{25}} x^6-688128 e^{\frac {24 c_1}{25}} x^5+573440 e^{\frac {24 c_1}{25}} x^4-286720 e^{\frac {24 c_1}{25}} x^3+86016 e^{\frac {24 c_1}{25}} x^2-14336 e^{\frac {24 c_1}{25}} x-32 x+1024 e^{\frac {24 c_1}{25}}+16\right ) \text {$\#$1}^7+\left (114688 e^{\frac {24 c_1}{25}} x^6-344064 e^{\frac {24 c_1}{25}} x^5+430080 e^{\frac {24 c_1}{25}} x^4-286720 e^{\frac {24 c_1}{25}} x^3+107520 e^{\frac {24 c_1}{25}} x^2-21504 e^{\frac {24 c_1}{25}} x+1792 e^{\frac {24 c_1}{25}}+16\right ) \text {$\#$1}^6+\left (-57344 e^{\frac {24 c_1}{25}} x^5+143360 e^{\frac {24 c_1}{25}} x^4-143360 e^{\frac {24 c_1}{25}} x^3+71680 e^{\frac {24 c_1}{25}} x^2-17920 e^{\frac {24 c_1}{25}} x+1792 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^5+\left (17920 e^{\frac {24 c_1}{25}} x^4-35840 e^{\frac {24 c_1}{25}} x^3+26880 e^{\frac {24 c_1}{25}} x^2-8960 e^{\frac {24 c_1}{25}} x+1120 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^4+\left (-3584 e^{\frac {24 c_1}{25}} x^3+5376 e^{\frac {24 c_1}{25}} x^2-2688 e^{\frac {24 c_1}{25}} x+448 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^3+\left (448 e^{\frac {24 c_1}{25}} x^2-448 e^{\frac {24 c_1}{25}} x+112 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^2+\left (16 e^{\frac {24 c_1}{25}}-32 e^{\frac {24 c_1}{25}} x\right ) \text {$\#$1}+e^{\frac {24 c_1}{25}}\& ,6\right ]}-1\right \},\left \{y(x)\to 3 x-\frac {1}{\text {Root}\left [\left (65536 e^{\frac {24 c_1}{25}} x^8-262144 e^{\frac {24 c_1}{25}} x^7+458752 e^{\frac {24 c_1}{25}} x^6-458752 e^{\frac {24 c_1}{25}} x^5+286720 e^{\frac {24 c_1}{25}} x^4-114688 e^{\frac {24 c_1}{25}} x^3+28672 e^{\frac {24 c_1}{25}} x^2+16 x^2-4096 e^{\frac {24 c_1}{25}} x-16 x+256 e^{\frac {24 c_1}{25}}+4\right ) \text {$\#$1}^8+\left (-131072 e^{\frac {24 c_1}{25}} x^7+458752 e^{\frac {24 c_1}{25}} x^6-688128 e^{\frac {24 c_1}{25}} x^5+573440 e^{\frac {24 c_1}{25}} x^4-286720 e^{\frac {24 c_1}{25}} x^3+86016 e^{\frac {24 c_1}{25}} x^2-14336 e^{\frac {24 c_1}{25}} x-32 x+1024 e^{\frac {24 c_1}{25}}+16\right ) \text {$\#$1}^7+\left (114688 e^{\frac {24 c_1}{25}} x^6-344064 e^{\frac {24 c_1}{25}} x^5+430080 e^{\frac {24 c_1}{25}} x^4-286720 e^{\frac {24 c_1}{25}} x^3+107520 e^{\frac {24 c_1}{25}} x^2-21504 e^{\frac {24 c_1}{25}} x+1792 e^{\frac {24 c_1}{25}}+16\right ) \text {$\#$1}^6+\left (-57344 e^{\frac {24 c_1}{25}} x^5+143360 e^{\frac {24 c_1}{25}} x^4-143360 e^{\frac {24 c_1}{25}} x^3+71680 e^{\frac {24 c_1}{25}} x^2-17920 e^{\frac {24 c_1}{25}} x+1792 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^5+\left (17920 e^{\frac {24 c_1}{25}} x^4-35840 e^{\frac {24 c_1}{25}} x^3+26880 e^{\frac {24 c_1}{25}} x^2-8960 e^{\frac {24 c_1}{25}} x+1120 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^4+\left (-3584 e^{\frac {24 c_1}{25}} x^3+5376 e^{\frac {24 c_1}{25}} x^2-2688 e^{\frac {24 c_1}{25}} x+448 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^3+\left (448 e^{\frac {24 c_1}{25}} x^2-448 e^{\frac {24 c_1}{25}} x+112 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^2+\left (16 e^{\frac {24 c_1}{25}}-32 e^{\frac {24 c_1}{25}} x\right ) \text {$\#$1}+e^{\frac {24 c_1}{25}}\& ,7\right ]}-1\right \},\left \{y(x)\to 3 x-\frac {1}{\text {Root}\left [\left (65536 e^{\frac {24 c_1}{25}} x^8-262144 e^{\frac {24 c_1}{25}} x^7+458752 e^{\frac {24 c_1}{25}} x^6-458752 e^{\frac {24 c_1}{25}} x^5+286720 e^{\frac {24 c_1}{25}} x^4-114688 e^{\frac {24 c_1}{25}} x^3+28672 e^{\frac {24 c_1}{25}} x^2+16 x^2-4096 e^{\frac {24 c_1}{25}} x-16 x+256 e^{\frac {24 c_1}{25}}+4\right ) \text {$\#$1}^8+\left (-131072 e^{\frac {24 c_1}{25}} x^7+458752 e^{\frac {24 c_1}{25}} x^6-688128 e^{\frac {24 c_1}{25}} x^5+573440 e^{\frac {24 c_1}{25}} x^4-286720 e^{\frac {24 c_1}{25}} x^3+86016 e^{\frac {24 c_1}{25}} x^2-14336 e^{\frac {24 c_1}{25}} x-32 x+1024 e^{\frac {24 c_1}{25}}+16\right ) \text {$\#$1}^7+\left (114688 e^{\frac {24 c_1}{25}} x^6-344064 e^{\frac {24 c_1}{25}} x^5+430080 e^{\frac {24 c_1}{25}} x^4-286720 e^{\frac {24 c_1}{25}} x^3+107520 e^{\frac {24 c_1}{25}} x^2-21504 e^{\frac {24 c_1}{25}} x+1792 e^{\frac {24 c_1}{25}}+16\right ) \text {$\#$1}^6+\left (-57344 e^{\frac {24 c_1}{25}} x^5+143360 e^{\frac {24 c_1}{25}} x^4-143360 e^{\frac {24 c_1}{25}} x^3+71680 e^{\frac {24 c_1}{25}} x^2-17920 e^{\frac {24 c_1}{25}} x+1792 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^5+\left (17920 e^{\frac {24 c_1}{25}} x^4-35840 e^{\frac {24 c_1}{25}} x^3+26880 e^{\frac {24 c_1}{25}} x^2-8960 e^{\frac {24 c_1}{25}} x+1120 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^4+\left (-3584 e^{\frac {24 c_1}{25}} x^3+5376 e^{\frac {24 c_1}{25}} x^2-2688 e^{\frac {24 c_1}{25}} x+448 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^3+\left (448 e^{\frac {24 c_1}{25}} x^2-448 e^{\frac {24 c_1}{25}} x+112 e^{\frac {24 c_1}{25}}\right ) \text {$\#$1}^2+\left (16 e^{\frac {24 c_1}{25}}-32 e^{\frac {24 c_1}{25}} x\right ) \text {$\#$1}+e^{\frac {24 c_1}{25}}\& ,8\right ]}-1\right \}\right \}\]

Maple ✓
cpu = 0.03 (sec), leaf count = 55

\[ \left \{ {\frac {1}{3}\ln \left ( {\frac {-2\,y \left ( x \right ) +4\,x-1}{-1+2\,x}} \right ) }-{\frac {4}{3}\ln \left ( {\frac {2-2\,y \left ( x \right ) -2\,x}{-1+2\,x}} \right ) }-\ln \left ( -1+2\,x \right ) -{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[(1 - 3*x + y[x])*y'[x] == 2*(x - y[x]),y[x],x]

Mathematica raw output

{{y[x] -> -1 + 3*x - Root[E^((24*C[1])/25) + (16*E^((24*C[1])/25) - 32*E^((24*C[
1])/25)*x)*#1 + (112*E^((24*C[1])/25) - 448*E^((24*C[1])/25)*x + 448*E^((24*C[1]
)/25)*x^2)*#1^2 + (448*E^((24*C[1])/25) - 2688*E^((24*C[1])/25)*x + 5376*E^((24*
C[1])/25)*x^2 - 3584*E^((24*C[1])/25)*x^3)*#1^3 + (1120*E^((24*C[1])/25) - 8960*
E^((24*C[1])/25)*x + 26880*E^((24*C[1])/25)*x^2 - 35840*E^((24*C[1])/25)*x^3 + 1
7920*E^((24*C[1])/25)*x^4)*#1^4 + (1792*E^((24*C[1])/25) - 17920*E^((24*C[1])/25
)*x + 71680*E^((24*C[1])/25)*x^2 - 143360*E^((24*C[1])/25)*x^3 + 143360*E^((24*C
[1])/25)*x^4 - 57344*E^((24*C[1])/25)*x^5)*#1^5 + (16 + 1792*E^((24*C[1])/25) - 
21504*E^((24*C[1])/25)*x + 107520*E^((24*C[1])/25)*x^2 - 286720*E^((24*C[1])/25)
*x^3 + 430080*E^((24*C[1])/25)*x^4 - 344064*E^((24*C[1])/25)*x^5 + 114688*E^((24
*C[1])/25)*x^6)*#1^6 + (16 + 1024*E^((24*C[1])/25) - 32*x - 14336*E^((24*C[1])/2
5)*x + 86016*E^((24*C[1])/25)*x^2 - 286720*E^((24*C[1])/25)*x^3 + 573440*E^((24*
C[1])/25)*x^4 - 688128*E^((24*C[1])/25)*x^5 + 458752*E^((24*C[1])/25)*x^6 - 1310
72*E^((24*C[1])/25)*x^7)*#1^7 + (4 + 256*E^((24*C[1])/25) - 16*x - 4096*E^((24*C
[1])/25)*x + 16*x^2 + 28672*E^((24*C[1])/25)*x^2 - 114688*E^((24*C[1])/25)*x^3 +
 286720*E^((24*C[1])/25)*x^4 - 458752*E^((24*C[1])/25)*x^5 + 458752*E^((24*C[1])
/25)*x^6 - 262144*E^((24*C[1])/25)*x^7 + 65536*E^((24*C[1])/25)*x^8)*#1^8 & , 1]
^(-1)}, {y[x] -> -1 + 3*x - Root[E^((24*C[1])/25) + (16*E^((24*C[1])/25) - 32*E^
((24*C[1])/25)*x)*#1 + (112*E^((24*C[1])/25) - 448*E^((24*C[1])/25)*x + 448*E^((
24*C[1])/25)*x^2)*#1^2 + (448*E^((24*C[1])/25) - 2688*E^((24*C[1])/25)*x + 5376*
E^((24*C[1])/25)*x^2 - 3584*E^((24*C[1])/25)*x^3)*#1^3 + (1120*E^((24*C[1])/25) 
- 8960*E^((24*C[1])/25)*x + 26880*E^((24*C[1])/25)*x^2 - 35840*E^((24*C[1])/25)*
x^3 + 17920*E^((24*C[1])/25)*x^4)*#1^4 + (1792*E^((24*C[1])/25) - 17920*E^((24*C
[1])/25)*x + 71680*E^((24*C[1])/25)*x^2 - 143360*E^((24*C[1])/25)*x^3 + 143360*E
^((24*C[1])/25)*x^4 - 57344*E^((24*C[1])/25)*x^5)*#1^5 + (16 + 1792*E^((24*C[1])
/25) - 21504*E^((24*C[1])/25)*x + 107520*E^((24*C[1])/25)*x^2 - 286720*E^((24*C[
1])/25)*x^3 + 430080*E^((24*C[1])/25)*x^4 - 344064*E^((24*C[1])/25)*x^5 + 114688
*E^((24*C[1])/25)*x^6)*#1^6 + (16 + 1024*E^((24*C[1])/25) - 32*x - 14336*E^((24*
C[1])/25)*x + 86016*E^((24*C[1])/25)*x^2 - 286720*E^((24*C[1])/25)*x^3 + 573440*
E^((24*C[1])/25)*x^4 - 688128*E^((24*C[1])/25)*x^5 + 458752*E^((24*C[1])/25)*x^6
 - 131072*E^((24*C[1])/25)*x^7)*#1^7 + (4 + 256*E^((24*C[1])/25) - 16*x - 4096*E
^((24*C[1])/25)*x + 16*x^2 + 28672*E^((24*C[1])/25)*x^2 - 114688*E^((24*C[1])/25
)*x^3 + 286720*E^((24*C[1])/25)*x^4 - 458752*E^((24*C[1])/25)*x^5 + 458752*E^((2
4*C[1])/25)*x^6 - 262144*E^((24*C[1])/25)*x^7 + 65536*E^((24*C[1])/25)*x^8)*#1^8
 & , 2]^(-1)}, {y[x] -> -1 + 3*x - Root[E^((24*C[1])/25) + (16*E^((24*C[1])/25) 
- 32*E^((24*C[1])/25)*x)*#1 + (112*E^((24*C[1])/25) - 448*E^((24*C[1])/25)*x + 4
48*E^((24*C[1])/25)*x^2)*#1^2 + (448*E^((24*C[1])/25) - 2688*E^((24*C[1])/25)*x 
+ 5376*E^((24*C[1])/25)*x^2 - 3584*E^((24*C[1])/25)*x^3)*#1^3 + (1120*E^((24*C[1
])/25) - 8960*E^((24*C[1])/25)*x + 26880*E^((24*C[1])/25)*x^2 - 35840*E^((24*C[1
])/25)*x^3 + 17920*E^((24*C[1])/25)*x^4)*#1^4 + (1792*E^((24*C[1])/25) - 17920*E
^((24*C[1])/25)*x + 71680*E^((24*C[1])/25)*x^2 - 143360*E^((24*C[1])/25)*x^3 + 1
43360*E^((24*C[1])/25)*x^4 - 57344*E^((24*C[1])/25)*x^5)*#1^5 + (16 + 1792*E^((2
4*C[1])/25) - 21504*E^((24*C[1])/25)*x + 107520*E^((24*C[1])/25)*x^2 - 286720*E^
((24*C[1])/25)*x^3 + 430080*E^((24*C[1])/25)*x^4 - 344064*E^((24*C[1])/25)*x^5 +
 114688*E^((24*C[1])/25)*x^6)*#1^6 + (16 + 1024*E^((24*C[1])/25) - 32*x - 14336*
E^((24*C[1])/25)*x + 86016*E^((24*C[1])/25)*x^2 - 286720*E^((24*C[1])/25)*x^3 + 
573440*E^((24*C[1])/25)*x^4 - 688128*E^((24*C[1])/25)*x^5 + 458752*E^((24*C[1])/
25)*x^6 - 131072*E^((24*C[1])/25)*x^7)*#1^7 + (4 + 256*E^((24*C[1])/25) - 16*x -
 4096*E^((24*C[1])/25)*x + 16*x^2 + 28672*E^((24*C[1])/25)*x^2 - 114688*E^((24*C
[1])/25)*x^3 + 286720*E^((24*C[1])/25)*x^4 - 458752*E^((24*C[1])/25)*x^5 + 45875
2*E^((24*C[1])/25)*x^6 - 262144*E^((24*C[1])/25)*x^7 + 65536*E^((24*C[1])/25)*x^
8)*#1^8 & , 3]^(-1)}, {y[x] -> -1 + 3*x - Root[E^((24*C[1])/25) + (16*E^((24*C[1
])/25) - 32*E^((24*C[1])/25)*x)*#1 + (112*E^((24*C[1])/25) - 448*E^((24*C[1])/25
)*x + 448*E^((24*C[1])/25)*x^2)*#1^2 + (448*E^((24*C[1])/25) - 2688*E^((24*C[1])
/25)*x + 5376*E^((24*C[1])/25)*x^2 - 3584*E^((24*C[1])/25)*x^3)*#1^3 + (1120*E^(
(24*C[1])/25) - 8960*E^((24*C[1])/25)*x + 26880*E^((24*C[1])/25)*x^2 - 35840*E^(
(24*C[1])/25)*x^3 + 17920*E^((24*C[1])/25)*x^4)*#1^4 + (1792*E^((24*C[1])/25) - 
17920*E^((24*C[1])/25)*x + 71680*E^((24*C[1])/25)*x^2 - 143360*E^((24*C[1])/25)*
x^3 + 143360*E^((24*C[1])/25)*x^4 - 57344*E^((24*C[1])/25)*x^5)*#1^5 + (16 + 179
2*E^((24*C[1])/25) - 21504*E^((24*C[1])/25)*x + 107520*E^((24*C[1])/25)*x^2 - 28
6720*E^((24*C[1])/25)*x^3 + 430080*E^((24*C[1])/25)*x^4 - 344064*E^((24*C[1])/25
)*x^5 + 114688*E^((24*C[1])/25)*x^6)*#1^6 + (16 + 1024*E^((24*C[1])/25) - 32*x -
 14336*E^((24*C[1])/25)*x + 86016*E^((24*C[1])/25)*x^2 - 286720*E^((24*C[1])/25)
*x^3 + 573440*E^((24*C[1])/25)*x^4 - 688128*E^((24*C[1])/25)*x^5 + 458752*E^((24
*C[1])/25)*x^6 - 131072*E^((24*C[1])/25)*x^7)*#1^7 + (4 + 256*E^((24*C[1])/25) -
 16*x - 4096*E^((24*C[1])/25)*x + 16*x^2 + 28672*E^((24*C[1])/25)*x^2 - 114688*E
^((24*C[1])/25)*x^3 + 286720*E^((24*C[1])/25)*x^4 - 458752*E^((24*C[1])/25)*x^5 
+ 458752*E^((24*C[1])/25)*x^6 - 262144*E^((24*C[1])/25)*x^7 + 65536*E^((24*C[1])
/25)*x^8)*#1^8 & , 4]^(-1)}, {y[x] -> -1 + 3*x - Root[E^((24*C[1])/25) + (16*E^(
(24*C[1])/25) - 32*E^((24*C[1])/25)*x)*#1 + (112*E^((24*C[1])/25) - 448*E^((24*C
[1])/25)*x + 448*E^((24*C[1])/25)*x^2)*#1^2 + (448*E^((24*C[1])/25) - 2688*E^((2
4*C[1])/25)*x + 5376*E^((24*C[1])/25)*x^2 - 3584*E^((24*C[1])/25)*x^3)*#1^3 + (1
120*E^((24*C[1])/25) - 8960*E^((24*C[1])/25)*x + 26880*E^((24*C[1])/25)*x^2 - 35
840*E^((24*C[1])/25)*x^3 + 17920*E^((24*C[1])/25)*x^4)*#1^4 + (1792*E^((24*C[1])
/25) - 17920*E^((24*C[1])/25)*x + 71680*E^((24*C[1])/25)*x^2 - 143360*E^((24*C[1
])/25)*x^3 + 143360*E^((24*C[1])/25)*x^4 - 57344*E^((24*C[1])/25)*x^5)*#1^5 + (1
6 + 1792*E^((24*C[1])/25) - 21504*E^((24*C[1])/25)*x + 107520*E^((24*C[1])/25)*x
^2 - 286720*E^((24*C[1])/25)*x^3 + 430080*E^((24*C[1])/25)*x^4 - 344064*E^((24*C
[1])/25)*x^5 + 114688*E^((24*C[1])/25)*x^6)*#1^6 + (16 + 1024*E^((24*C[1])/25) -
 32*x - 14336*E^((24*C[1])/25)*x + 86016*E^((24*C[1])/25)*x^2 - 286720*E^((24*C[
1])/25)*x^3 + 573440*E^((24*C[1])/25)*x^4 - 688128*E^((24*C[1])/25)*x^5 + 458752
*E^((24*C[1])/25)*x^6 - 131072*E^((24*C[1])/25)*x^7)*#1^7 + (4 + 256*E^((24*C[1]
)/25) - 16*x - 4096*E^((24*C[1])/25)*x + 16*x^2 + 28672*E^((24*C[1])/25)*x^2 - 1
14688*E^((24*C[1])/25)*x^3 + 286720*E^((24*C[1])/25)*x^4 - 458752*E^((24*C[1])/2
5)*x^5 + 458752*E^((24*C[1])/25)*x^6 - 262144*E^((24*C[1])/25)*x^7 + 65536*E^((2
4*C[1])/25)*x^8)*#1^8 & , 5]^(-1)}, {y[x] -> -1 + 3*x - Root[E^((24*C[1])/25) + 
(16*E^((24*C[1])/25) - 32*E^((24*C[1])/25)*x)*#1 + (112*E^((24*C[1])/25) - 448*E
^((24*C[1])/25)*x + 448*E^((24*C[1])/25)*x^2)*#1^2 + (448*E^((24*C[1])/25) - 268
8*E^((24*C[1])/25)*x + 5376*E^((24*C[1])/25)*x^2 - 3584*E^((24*C[1])/25)*x^3)*#1
^3 + (1120*E^((24*C[1])/25) - 8960*E^((24*C[1])/25)*x + 26880*E^((24*C[1])/25)*x
^2 - 35840*E^((24*C[1])/25)*x^3 + 17920*E^((24*C[1])/25)*x^4)*#1^4 + (1792*E^((2
4*C[1])/25) - 17920*E^((24*C[1])/25)*x + 71680*E^((24*C[1])/25)*x^2 - 143360*E^(
(24*C[1])/25)*x^3 + 143360*E^((24*C[1])/25)*x^4 - 57344*E^((24*C[1])/25)*x^5)*#1
^5 + (16 + 1792*E^((24*C[1])/25) - 21504*E^((24*C[1])/25)*x + 107520*E^((24*C[1]
)/25)*x^2 - 286720*E^((24*C[1])/25)*x^3 + 430080*E^((24*C[1])/25)*x^4 - 344064*E
^((24*C[1])/25)*x^5 + 114688*E^((24*C[1])/25)*x^6)*#1^6 + (16 + 1024*E^((24*C[1]
)/25) - 32*x - 14336*E^((24*C[1])/25)*x + 86016*E^((24*C[1])/25)*x^2 - 286720*E^
((24*C[1])/25)*x^3 + 573440*E^((24*C[1])/25)*x^4 - 688128*E^((24*C[1])/25)*x^5 +
 458752*E^((24*C[1])/25)*x^6 - 131072*E^((24*C[1])/25)*x^7)*#1^7 + (4 + 256*E^((
24*C[1])/25) - 16*x - 4096*E^((24*C[1])/25)*x + 16*x^2 + 28672*E^((24*C[1])/25)*
x^2 - 114688*E^((24*C[1])/25)*x^3 + 286720*E^((24*C[1])/25)*x^4 - 458752*E^((24*
C[1])/25)*x^5 + 458752*E^((24*C[1])/25)*x^6 - 262144*E^((24*C[1])/25)*x^7 + 6553
6*E^((24*C[1])/25)*x^8)*#1^8 & , 6]^(-1)}, {y[x] -> -1 + 3*x - Root[E^((24*C[1])
/25) + (16*E^((24*C[1])/25) - 32*E^((24*C[1])/25)*x)*#1 + (112*E^((24*C[1])/25) 
- 448*E^((24*C[1])/25)*x + 448*E^((24*C[1])/25)*x^2)*#1^2 + (448*E^((24*C[1])/25
) - 2688*E^((24*C[1])/25)*x + 5376*E^((24*C[1])/25)*x^2 - 3584*E^((24*C[1])/25)*
x^3)*#1^3 + (1120*E^((24*C[1])/25) - 8960*E^((24*C[1])/25)*x + 26880*E^((24*C[1]
)/25)*x^2 - 35840*E^((24*C[1])/25)*x^3 + 17920*E^((24*C[1])/25)*x^4)*#1^4 + (179
2*E^((24*C[1])/25) - 17920*E^((24*C[1])/25)*x + 71680*E^((24*C[1])/25)*x^2 - 143
360*E^((24*C[1])/25)*x^3 + 143360*E^((24*C[1])/25)*x^4 - 57344*E^((24*C[1])/25)*
x^5)*#1^5 + (16 + 1792*E^((24*C[1])/25) - 21504*E^((24*C[1])/25)*x + 107520*E^((
24*C[1])/25)*x^2 - 286720*E^((24*C[1])/25)*x^3 + 430080*E^((24*C[1])/25)*x^4 - 3
44064*E^((24*C[1])/25)*x^5 + 114688*E^((24*C[1])/25)*x^6)*#1^6 + (16 + 1024*E^((
24*C[1])/25) - 32*x - 14336*E^((24*C[1])/25)*x + 86016*E^((24*C[1])/25)*x^2 - 28
6720*E^((24*C[1])/25)*x^3 + 573440*E^((24*C[1])/25)*x^4 - 688128*E^((24*C[1])/25
)*x^5 + 458752*E^((24*C[1])/25)*x^6 - 131072*E^((24*C[1])/25)*x^7)*#1^7 + (4 + 2
56*E^((24*C[1])/25) - 16*x - 4096*E^((24*C[1])/25)*x + 16*x^2 + 28672*E^((24*C[1
])/25)*x^2 - 114688*E^((24*C[1])/25)*x^3 + 286720*E^((24*C[1])/25)*x^4 - 458752*
E^((24*C[1])/25)*x^5 + 458752*E^((24*C[1])/25)*x^6 - 262144*E^((24*C[1])/25)*x^7
 + 65536*E^((24*C[1])/25)*x^8)*#1^8 & , 7]^(-1)}, {y[x] -> -1 + 3*x - Root[E^((2
4*C[1])/25) + (16*E^((24*C[1])/25) - 32*E^((24*C[1])/25)*x)*#1 + (112*E^((24*C[1
])/25) - 448*E^((24*C[1])/25)*x + 448*E^((24*C[1])/25)*x^2)*#1^2 + (448*E^((24*C
[1])/25) - 2688*E^((24*C[1])/25)*x + 5376*E^((24*C[1])/25)*x^2 - 3584*E^((24*C[1
])/25)*x^3)*#1^3 + (1120*E^((24*C[1])/25) - 8960*E^((24*C[1])/25)*x + 26880*E^((
24*C[1])/25)*x^2 - 35840*E^((24*C[1])/25)*x^3 + 17920*E^((24*C[1])/25)*x^4)*#1^4
 + (1792*E^((24*C[1])/25) - 17920*E^((24*C[1])/25)*x + 71680*E^((24*C[1])/25)*x^
2 - 143360*E^((24*C[1])/25)*x^3 + 143360*E^((24*C[1])/25)*x^4 - 57344*E^((24*C[1
])/25)*x^5)*#1^5 + (16 + 1792*E^((24*C[1])/25) - 21504*E^((24*C[1])/25)*x + 1075
20*E^((24*C[1])/25)*x^2 - 286720*E^((24*C[1])/25)*x^3 + 430080*E^((24*C[1])/25)*
x^4 - 344064*E^((24*C[1])/25)*x^5 + 114688*E^((24*C[1])/25)*x^6)*#1^6 + (16 + 10
24*E^((24*C[1])/25) - 32*x - 14336*E^((24*C[1])/25)*x + 86016*E^((24*C[1])/25)*x
^2 - 286720*E^((24*C[1])/25)*x^3 + 573440*E^((24*C[1])/25)*x^4 - 688128*E^((24*C
[1])/25)*x^5 + 458752*E^((24*C[1])/25)*x^6 - 131072*E^((24*C[1])/25)*x^7)*#1^7 +
 (4 + 256*E^((24*C[1])/25) - 16*x - 4096*E^((24*C[1])/25)*x + 16*x^2 + 28672*E^(
(24*C[1])/25)*x^2 - 114688*E^((24*C[1])/25)*x^3 + 286720*E^((24*C[1])/25)*x^4 - 
458752*E^((24*C[1])/25)*x^5 + 458752*E^((24*C[1])/25)*x^6 - 262144*E^((24*C[1])/
25)*x^7 + 65536*E^((24*C[1])/25)*x^8)*#1^8 & , 8]^(-1)}}

Maple raw input

dsolve((1-3*x+y(x))*diff(y(x),x) = 2*x-2*y(x), y(x),'implicit')

Maple raw output

1/3*ln((-2*y(x)+4*x-1)/(-1+2*x))-4/3*ln((2-2*y(x)-2*x)/(-1+2*x))-ln(-1+2*x)-_C1 
= 0