Question

Linear
equations
y²dx
+ (x²-xy-y2) dy = 0 solve by integrating factor
​

Answer 1

Answer:

I am in 4 th class so I don't know this question answer

Answer 2

Answer:

Use a substitution: ⎧⎩⎨⎪⎪u=yxy=uxdy=udx+xdu  

y2dx+(x2−xy−y2)dy=0

(ux)2dx+(x2−x(ux)−(ux)2)(udx+xdu)=0

u2x2dx+x2(1−u−u2)(udx+xdu)=0

u2dx+(1−u−u2)(udx+xdu)=0

(u2+u−u2−u3)dx+x(1−u−u2)du

(u−u3)dx=−x(1−u−u2)du

1xdx=−1−u−u2u−u3

1xdx=12(1u+1−1u−1−2u)du

∫2xdx=∫(1u+1−1u−1−2u)du

2lnx=ln|u+1|−ln|u−1|−2ln|u|+C0

lnx2+lnu2+ln|u−1|−ln|u+1|=C0

lnx2+lny2x2+ln∣∣yx−1∣∣−ln∣∣yx+1∣∣=C0

ln∣∣y2(y−x)y+x∣∣=C0

y2(y−x)y+x=C

Step-by-step explanation: