Identify the type of the differential equation (as linear, homogeneous,exact, separable or Bernoulli) and find its general solutiondxdt = 2x + etx32
Question
Identify the type of the differential equation (as linear, homogeneous, exact, separable or Bernoulli) and find its general solution
\frac{dx}{dt} = 2x + e^{t} x^{3/2}
Solution
The given differential equation is:
dx/dt = 2x + e^(t/x^3/2)
This is a first order non-linear differential equation. It is not linear, not homogeneous, not exact, not separable, and not a Bernoulli equation.
Finding a general solution for this type of differential equation is not straightforward and usually requires special methods or numerical solutions. It's beyond the scope of basic calculus or differential equations courses.
If you have a specific method you'd like to use to solve this, or if there's more context to the problem, I'd be happy to help further!
Similar Questions
Identify the type of the differential equation (as linear, homogeneous,exact, separable or Bernoulli) and find its general solutiondxdt = 2x + etx32
Find the general solution of the following differential equations using the method of undeter-mined coefficientsy′′ − 2y′ + y = ex + x2
Linear differential equations (Review), equation reducible to linear form,Bernoulli‘sequation
The general solution of the ode dydx+1xy=2x2𝑑𝑦𝑑𝑥+1𝑥𝑦=2𝑥2 isa.yx=x42+c𝑦𝑥=𝑥42+𝑐b.yx=x42𝑦𝑥=𝑥42c.yx=x33+c𝑦𝑥=𝑥33+𝑐d.yx=x44+c
Find the general solution of each of the equation if one solution is given (i) xy′′ + (2x + 1)y′ + (x + 1)y = 0, y1(x) = e −x
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.