(y(x) − 3x + 1)y′(x) = 2(x −y(x))

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, $y^{'} (x) = f (\frac{X_{1}}{X_{2}})$

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

${{y (x) \to 3 x - \frac{1}{Root [(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) {# 1}^{8} + (- 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) {# 1}^{7} + (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) {# 1}^{6} + (- 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}}) {# 1}^{5} + (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}}) {# 1}^{4} + (- 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}}) {# 1}^{3} + (448 e^{\frac{24 c_{1}}{25}} x^{2} - 448 e^{\frac{24 c_{1}}{25}} x + 112 e^{\frac{24 c_{1}}{25}}) {# 1}^{2} + (16 e^{\frac{24 c_{1}}{25}} - 32 e^{\frac{24 c_{1}}{25}} x) # 1 + e^{\frac{24 c_{1}}{25}} &, 1]} - 1}, {y (x) \to 3 x - \frac{1}{Root [(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) {# 1}^{8} + (- 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) {# 1}^{7} + (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) {# 1}^{6} + (- 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}}) {# 1}^{5} + (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}}) {# 1}^{4} + (- 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}}) {# 1}^{3} + (448 e^{\frac{24 c_{1}}{25}} x^{2} - 448 e^{\frac{24 c_{1}}{25}} x + 112 e^{\frac{24 c_{1}}{25}}) {# 1}^{2} + (16 e^{\frac{24 c_{1}}{25}} - 32 e^{\frac{24 c_{1}}{25}} x) # 1 + e^{\frac{24 c_{1}}{25}} &, 2]} - 1}, {y (x) \to 3 x - \frac{1}{Root [(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) {# 1}^{8} + (- 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) {# 1}^{7} + (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) {# 1}^{6} + (- 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}}) {# 1}^{5} + (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}}) {# 1}^{4} + (- 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}}) {# 1}^{3} + (448 e^{\frac{24 c_{1}}{25}} x^{2} - 448 e^{\frac{24 c_{1}}{25}} x + 112 e^{\frac{24 c_{1}}{25}}) {# 1}^{2} + (16 e^{\frac{24 c_{1}}{25}} - 32 e^{\frac{24 c_{1}}{25}} x) # 1 + e^{\frac{24 c_{1}}{25}} &, 3]} - 1}, {y (x) \to 3 x - \frac{1}{Root [(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) {# 1}^{8} + (- 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) {# 1}^{7} + (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) {# 1}^{6} + (- 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}}) {# 1}^{5} + (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}}) {# 1}^{4} + (- 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}}) {# 1}^{3} + (448 e^{\frac{24 c_{1}}{25}} x^{2} - 448 e^{\frac{24 c_{1}}{25}} x + 112 e^{\frac{24 c_{1}}{25}}) {# 1}^{2} + (16 e^{\frac{24 c_{1}}{25}} - 32 e^{\frac{24 c_{1}}{25}} x) # 1 + e^{\frac{24 c_{1}}{25}} &, 4]} - 1}, {y (x) \to 3 x - \frac{1}{Root [(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) {# 1}^{8} + (- 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) {# 1}^{7} + (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) {# 1}^{6} + (- 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}}) {# 1}^{5} + (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}}) {# 1}^{4} + (- 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}}) {# 1}^{3} + (448 e^{\frac{24 c_{1}}{25}} x^{2} - 448 e^{\frac{24 c_{1}}{25}} x + 112 e^{\frac{24 c_{1}}{25}}) {# 1}^{2} + (16 e^{\frac{24 c_{1}}{25}} - 32 e^{\frac{24 c_{1}}{25}} x) # 1 + e^{\frac{24 c_{1}}{25}} &, 5]} - 1}, {y (x) \to 3 x - \frac{1}{Root [(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) {# 1}^{8} + (- 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) {# 1}^{7} + (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) {# 1}^{6} + (- 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}}) {# 1}^{5} + (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}}) {# 1}^{4} + (- 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}}) {# 1}^{3} + (448 e^{\frac{24 c_{1}}{25}} x^{2} - 448 e^{\frac{24 c_{1}}{25}} x + 112 e^{\frac{24 c_{1}}{25}}) {# 1}^{2} + (16 e^{\frac{24 c_{1}}{25}} - 32 e^{\frac{24 c_{1}}{25}} x) # 1 + e^{\frac{24 c_{1}}{25}} &, 6]} - 1}, {y (x) \to 3 x - \frac{1}{Root [(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) {# 1}^{8} + (- 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) {# 1}^{7} + (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) {# 1}^{6} + (- 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}}) {# 1}^{5} + (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}}) {# 1}^{4} + (- 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}}) {# 1}^{3} + (448 e^{\frac{24 c_{1}}{25}} x^{2} - 448 e^{\frac{24 c_{1}}{25}} x + 112 e^{\frac{24 c_{1}}{25}}) {# 1}^{2} + (16 e^{\frac{24 c_{1}}{25}} - 32 e^{\frac{24 c_{1}}{25}} x) # 1 + e^{\frac{24 c_{1}}{25}} &, 7]} - 1}, {y (x) \to 3 x - \frac{1}{Root [(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) {# 1}^{8} + (- 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) {# 1}^{7} + (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) {# 1}^{6} + (- 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}}) {# 1}^{5} + (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}}) {# 1}^{4} + (- 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}}) {# 1}^{3} + (448 e^{\frac{24 c_{1}}{25}} x^{2} - 448 e^{\frac{24 c_{1}}{25}} x + 112 e^{\frac{24 c_{1}}{25}}) {# 1}^{2} + (16 e^{\frac{24 c_{1}}{25}} - 32 e^{\frac{24 c_{1}}{25}} x) # 1 + e^{\frac{24 c_{1}}{25}} &, 8]} - 1}}$

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

${\frac{1}{3} \ln (\frac{- 2 y (x) + 4 x - 1}{- 1 + 2 x}) - \frac{4}{3} \ln (\frac{2 - 2 y (x) - 2 x}{- 1 + 2 x}) - \ln (- 1 + 2 x) -_C 1 = 0}$ 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

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4.10.4 (y(x)−3x+1)y′(x)=2(x−y(x))

4.10.4 $(y (x) - 3 x + 1) y^{'} (x) = 2 (x - y (x))$