Question:
The solution of the differential equation x (dy)/(dx) = y + x tan (y)/(x), is
The solution of the differential equation x (dy)/(dx) = y + x tan (y)/(x), is
Options:
- sin(y/x) = cx
- sin(x/y) = x + C
- sin(x/y) = Cy
- sin(y/x) = Cy
- sin(y/x) = cx
- sin(x/y) = x + C
- sin(x/y) = Cy
- sin(y/x) = Cy
Correct Answer: d)
Explanation:
1 We ha√e , 1
J dy y
H *E = y+ ztan(L) ,
y _y y
‘ ⇒ L=371 tan(Z) (c)) ‘
Put £ =√
B
yew
‘ Differentiating on both sides,
dy d√
—=√+zT=
dz dz
√+tano =√ + zl …from (i)
_ di
H tan√ = zg ,
‘ 42 — cot √d√ ‘
1 4 = cot√dy
‘ log x + log C = log sin V ‘
‘ Cx=sin√ !
1 sin (2) =CcX 1
hon a
10s. ‘
‘ @y”-y=-6y=0
1
1 We ha√e , 1
J dy y
H *E = y+ ztan(L) ,
y _y y
‘ ⇒ L=371 tan(Z) (c)) ‘
Put £ =√
B
yew
‘ Differentiating on both sides,
dy d√
—=√+zT=
dz dz
√+tano =√ + zl …from (i)
_ di
H tan√ = zg ,
‘ 42 — cot √d√ ‘
1 4 = cot√dy
‘ log x + log C = log sin V ‘
‘ Cx=sin√ !
1 sin (2) =CcX 1
hon a
10s. ‘
‘ @y”-y=-6y=0
1