Differential Equations Answers

simultaneous differential equations

1. dx/dt=2x
dy/dt=4y


2. dx/dt=2x
dy/dt=2y

determine the orthogonal trajectory of families. (illustrate)

1. x^2+y^2+2ay-1=0
2. y=a(e^(-2x))

differential equations in the form of F(x,y,p), F(y/x,p) or differential equations containing p(p=dy/dx)

1. 4y(p^2)+2xp-y=0
2. (x^2)(p^2)+3xyp+2(y^2)=0
3. (x^2)(p^2)-(2(xy-2)p)+2(y^2)=0

differential equations in the form of F(x,y,p), F(y/x,p) or differential equations containing p(p=dy/dx)

1. (y-xp)^2=b^2+a^2 p^2
2. y^2 p^2+4y^2-(x+yp)^2=0

(2x+y+3)×(dy/dx)=(x+2y+1)

form differential for y=ax^3+bx^2 ?

(x^2+y^2)dx−2xydy=0
a. x+y/x=c
b. x-y/x=c
c. x-y^2/x=c
d. x+y^2/x=c

I need answer for it (D^2+2DD'+D'^2-2D-2D') z=sin(x+2y)

Transform the parabolic equations
4Uxx + 12Uxy + 9Uyy − 2Ux + U = 0

A. uξξ −1/3uη +1/9u = −
B. uξξ −1/3uη +1/9u = 0
C. uξξ − uηu=0
D. uξξ−1/5uηξ +1/2u=0

4. dy/dx=2y^2+3xy
x^2

y=\frac{c x^{3}}{1-c x^{2}}\]
y=cx31+cx2
y=−cx31−cx2
y=−cx31+cx2