Solving Linear Differential Equations of First Order
Trending Questions
Q. The curves satisfying the differential equation (1−x2)y1+xy=ax are
- ellipses and hyperbolas
- ellipses and parabola
- ellipses and straight lines
- circles and ellipses
Q. The solution of y2−7y1+12y=0 is
- y=C1e3x+C2e4x
- None of these
- y=C1e3x+C2xe4x
- y=C1xe3x+C2e4x
Q. The solution of (x+2y3)(dydx)=y is (where c is arbitrary constant)
- x=y3+cy
- x=y3−cy
- y=y3−cy
- y=y3+cy
Q. Solution of the differential equation
cosxdy=y(sin x−y)dx, 0<x<π2 is
cosxdy=y(sin x−y)dx, 0<x<π2 is
- ysec x=tan x+c
- ytan x=sec x+c
- tan x=(sec x+c)y
- sec x=(tan x+c)y
Q.
The solution of the differential equation x dydx+y=x2+3x+2 is
xy=x33+32x2+2x+c
xy=x44+x3+x2+c
xy=x44+33x2+c
xy=x44+x3+x2+cx
Q. If y1(x) is a solution of the differential equation dydx+f(x)y=0, then a solution of differential equation dydx+f(x)y=r(x) is
- 1y(x)∫y1(x)dx
- y1(x)∫r(x)y1(x)dx+c
- intr(x)y1(x)dx
- none of these
Q.
The solution of the equation dydx+y tan x=xm cos x is
- (m+1)y=xm+1cos x+c(m+1)cos x
- (my=(xm+c)cos x
- y=(xm+1+c)cos x
None of these
Q.
Let f:R+→R+ be a differentiable function satisfying f(xy)=f(x)y+f(y)x for all x, yϵR+. Also f(1)=0, f′(1)=1. If M is the greatest value of f(x) then [m+e] is ___ (where [.] represents Greatest Integer Function).
3
2
1
0
Q. The solution of y2−7y1+12y=0 is
- y=C1e3x+C2e4x
- y=C1xe3x+C2e4x
- y=C1e3x+C2xe4x
- None of these
Q.
The solution of the differential equation dydx+3x21+x3 y=sin2 x1+x3 is
y(1+x3)=x+12 sin 2x+c
2 tan−1(xy)+log x+c=0
log(y+√x2+y2)+log y+c=0
sin h−1(xy)+log y+c=0