The equation z = ax +
+a2y2 +b is solution
Answers
Answer:
The Solution of the Initial Value Problem sin(x)dx + ydy = 0 , where y(0) = 1 is
(a)y =
p
2 sin(x) − 1 (b) y =p
2 cos(x) − 1
(c)y =
p
2 sin(x) + 1 (d) y =p
2 cos(x) + 1
Answer: (b)
Hint: Again by Variable Separable method then integrate and find out the integrating
constant by the given Initial condition.
(3) Let y1 and y2 be the solution of dy
dx = y + 17 with Initial Condition y1(0) = 0 and
y2(0) = 1 then
(a)y1 and y2 will never Intersect (b) y1 and y2 will Intersect at x = 17
(c)y1 and y2 will Intersect at x = 1 (d) None of the Above
Answer: (a)
Hint: Use the intial condition to find constants and draw the the graph of the two
different solutions .
(4) The Diff. Eq. y
0
= 60(y
2
)) 1
5 ; x > 0 y(0) = 0 has
(a) Unique Solution (b) Two Solution
(c) No Solution (d) Infinite Number of Solutions
Answer: (b)
Hint: Variable Separable Method
(5) The solution of the exact Differential equation (3x
2
y
2+x
2
)dx+(2x3y+y
2
)dy = 0 is
(a) x
3
y
2 +
x
3
3 +
y
3
3 = c (b) x
3
y
2 −
x
3
3 +
y
3
3 = c
(c)x
3
y
3 +
x
3
3 +
y
3
3 = c (d) x
3
y
2 + x
3 +
y
3
3 = c
Answer: (a)
Hint: The Equation is given to be exact . Use the formula to find the solution.
(6) Which function is a solution to yy
0
− sin ty = t
2
sin t cost
(a) y = t cost (b) y = tsin t (c) y = cost
(d) y = sin t (e) y = t
2
sin t cost (f) None of the Above