Differential Equation

In this page, we solve dy/dx+y/x=x^2y^6. This is a Bernoulli’s differential equation. The general solution of dy/dx+y/x=x^2y^6 is 5x3y5 + Cx5y5 = 2 where C denotes an arbitrary constant of integrals. Let us now solve the Bernoulli’s differential equation dy/dx+y/x=x2y6. Solution of dy/dx+y/x=x^2y^6 Question: Find the solution of $\dfrac{dy}{dx}+\dfrac{y}{x}=x^2y^6$. Answer: $\dfrac{dy}{dx}+\dfrac{y}{x}=x^2y^6$ …(I) The given differential … Read more

The general solution of (D2+4)y=cos2x is given by y=c1cos2x + c2sin2x + (1+xsin2x)/8. Lets learn how to solve (D^2+4)y=cos^2x. As D2 = d2/dx2, the differential equation (D2+4)y=cos2x can also be written as follows: d2y/dx2 + 4y = cos2x. Solve (D2+4)y=cos^2x Question: Solve the equation $\dfrac{d^2y}{dx^2} + 4y = \cos^2x$. Solution: Letting D2 = d2/dx2, we … Read more

Here we learn how to solve (D^2+4)y=sin^2x. The general solution of (D2+4)y=sin2x is given by y=c1cos2x + c2sin2x + (1-xsin2x)/8. The differential equation (D2+4)y=sin2x can also be written as follows: d2y/dx2 + 4y = sin2x. Now let us solve this equation. Solve (D2+4)y=sin^2x Question: Solve the equation $\dfrac{d^2y}{dx^2} + 4y = \sin^2x$. Solution: One can … Read more

Here we solve the equation d^2y/dx^2+4y=cos2x, that is, Solve (D^2+4)y=cos2x. The general solution of d2y/dx2 + 4y = cos2x is equal to y=c1cos2x + c2sin2x + (xsin2x)/4. Solve (D2+4)y=cos2x Question: Solve the equation $\dfrac{d^2y}{dx^2}$ + 4y = cos2x. Solution: Letting D2 = d2/dx2, we can write the given differential equation as follows: (D2+4)y = cos2x … Read more

Here we solve (D^2+4)y=sin2x. The general solution of d2y/dx2 + 4y = sin2x is given by y=c1cos2x + c2sin2x – (xcos2x)/4. In this page, let us learn to solve the equation d^2y/dx^2+4y=sin2x, i.e, (D^2+4)y=sin2x. Solve (D2+4)y=sin2x Question: Solve the equation $\dfrac{d^2y}{dx^2}$ + 4y = sin2x. Solution: The given differential equation can be written in the … Read more

The general solution of the differential equation dy/dx = xy2 is given by y=-2/(x2+2K) where K is an arbitrary constant. Here we will learn how to find the general solution of the differential equation. Set C=2K. Answer: the solution of $\dfrac{dy}{dx}=xy^2$ is given by y = $-\dfrac{2}{x^2+C}$. Solve dy/dx=xy2 Given $\dfrac{dy}{dx}=xy^2$ To solve it, we … Read more

The general solution of the differential equation dy/dx+ytanx = secx is equal to ysecx =tanx +C where C is a constant. This equation is an example of a first order linear ordinary differential equation. Solve dy/dx+ytanx = secx Question: Solve the differential equation $\dfrac{dy}{dx}$+ytanx = secx. Solution: The given equation has the form $\dfrac{dy}{dx}+P(x)=Q(x)$, a … Read more

The general solution of the differential equation (x+y+1)dy/dx=1 is equal to x= -(y+2)+Cey where C denotes an arbitrary constant. Here we will learn how to solve the differential equation (x+y+1)dy/dx=1. Solve (x+y+1)dy/dx=1 Question: What is the solution of (x+y+1)$\dfrac{dy}{dx}$=1? Answer: Let us put x+y+1 = v. Differentiating w.r.t x, we get that $1+\dfrac{dy}{dx}=\dfrac{dv}{dx}$ ⇒ $\dfrac{dy}{dx}=\dfrac{dv}{dx}-1$ … Read more

The general solution of the differential equation dy/dx=x-y is equal to y=x-1-Ce-x where C is an arbitrary constant. In this post, we will learn how to find the general solution of dy/dx =x-y. Solution of dy/dx=x-y Question: Find the genral solution of $\dfrac{dy}{dx}$ =x-y. Solution: Let x-y=v. Differentiating w.r.t x, we get that $1-\dfrac{dy}{dx}=\dfrac{dv}{dx}$ ⇒ … Read more

The general solution of the differential equation dy/dx =sec(x+y) is equal to y =tan (x+y)/2 +C where C denotes an arbitrary constant. In this post, we will learn how to find the general solution of dy/dx=sec(x+y). Solve dy/dx=sec(x+y) Question: What is the general solution of $\dfrac{dy}{dx}$ =sec(x+y)? Answer: Put x+y=v, so that $1+\dfrac{dy}{dx}=\dfrac{dv}{dx}$. ⇒ $\dfrac{dy}{dx}=\dfrac{dv}{dx}-1$ … Read more