Question

find the general solution dy/dx=(y-x) ^2 by substitution​

Answer 1

Step-by-step explanation:

Let t=x−y⟹dtdx=1−dydx∴dydx=1−dtdx

1−dtdxdtdxdt1−t2∫dt1−t2∫dt(1−t)(1+t)12∫(1−t)+(1+t)(1−t)(1+t)dt∫dt1+t+∫dt1−tln|1+t|−ln|1−t|+C3ln|1+t1−t|−2x+C4ln|1+x−y1−x+y|−2x+C4=t2=1−t2=dx=∫dx=x+C1=x+C1=2x+C2=2x+C2=0=0