hi guys need some help on diff eqn, ive done the workingout(adsbygoogle = window.adsbygoogle || []).push({});

and answers but not sure if they are right mind if someone

can check them for me thanks

Find the general solution of the differential equation

dy/dx - 2y = e^(5x)

i found I(x) = e^ integral (-2 dx) = e^(-2x)

as I(x) = e^Integral (p(x)) in this case p=-2

therfore d/dx((e^-2x)*y) = e^(3x) // as we multiply both sides by e^(-2x)

therefore e^(-2x)y = integral e^(3x)

e^(-2x)y = e^(3x)/3 + C

y= e^(3x)/(3*e^(-2x)) + C

y= 1/3e^(5x) + Ce^(2x)

2.

given that z=2xt^3 - cos5x and x^3 + t^2 = 6x

find dz/dt using a chain rule

i will use notatio 9 as the "day symbol"

dz/dt = 9z/9x*dx/dt + dz/dt

= (2t^3 + 5sin5x)*dx/dt + 6xt^2 !!(3)!!

then knowing

x^3 + t^2 = 6x i diff resp to x so

3x^2*dx/dt - 6dx/dt = -2t

dx/dt = 2t/(3x^2 - 6)

i subtituted this back into (3) and got

= (4t^4 + 10tsin5x + 18x^3t^2 - 36xt^2) / (3x^2-6)

3. given that z=e^(5x)sin2y and y=x^2 + 5

find dz/dx as a function of x using a chain rule

same 9 symbol represtn day

dz/dx=9z/9x + 9z/9y*dy\dx

dz/dx = 5e^(5x)sin2y + 2xe^(5x)cos2y

i subtitued y=x^2 + 5 and got this

dx/dx = e^(5x) * [5sin(2x^2+10) + 2xcos(2x^2 + 10) ]

so i hope i did it right

thanks for the help guys

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Second order differential equations!

**Physics Forums | Science Articles, Homework Help, Discussion**