Differential Equations Answers

Linear differential equation with constant coefficient

d³y/dx³-13dy/dx+12y

Using power series method solve the equation

y''+9y=0

Using Charpit’s method, find a complete integral of the following equations: xpq + yq^2 = 1

Eliminate the arbitrary constants indicated in brackets from the following equation

and form corresponding partial differential equation:

e

1

{z−(

x2

y

)}

=

ax

2

y2 +

b

y

;(a,b)

Using Charpit’s method, find a complete integral of the following equations: xpq + yq^2 = 1

Find particular integrals of the following partial differential equation to represent

surfaces passing through the following curve:

(𝑦 – 𝑧)𝑝 + (𝑧 – 𝑥)𝑞 = 𝑥 – 𝑦 ; 𝑧 = 0, 𝑦 = 2𝑥

Eliminate the arbitrary function and hence obtain the partial differential equation:

φ (
z
x
3
,
y
x
) = 0

Show that the partial differential equations

z = px + qy and 2xy(p² + q²) = z(yp + xq)are compatible

Show that the partial differential equations

z = px + qy and 2xy(p² + q²) = z(yp + xq)are compatible

(z²d²÷dz²)w+3÷16(1+z)w=0