Differential Equation

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 ${\displaystyle \frac{dy}{dx}}=x{y}^2$ is given by y = $-{\displaystyle \frac{2}{x^2+C}}$. Solve dy/dx=xy2 Given ${\displaystyle \frac{dy}{dx}}=x{y}^2$ 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 ${\displaystyle \frac{dy}{dx}}$+ytanx = secx. Solution: The given equation has the form ${\displaystyle \frac{dy}{dx}}+P(x)=Q(x)$, 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)${\displaystyle \frac{dy}{dx}}$=1? Answer: Let us put x+y+1 = v. Differentiating w.r.t x, we get that $1+{\displaystyle \frac{dy}{dx}}={\displaystyle \frac{dv}{dx}}$ ⇒ ${\displaystyle \frac{dy}{dx}}={\displaystyle \frac{dv}{dx}}-1$ … 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 ${\displaystyle \frac{dy}{dx}}$ =x-y. Solution: Let x-y=v. Differentiating w.r.t x, we get that $1-{\displaystyle \frac{dy}{dx}}={\displaystyle \frac{dv}{dx}}$ ⇒ … 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 ${\displaystyle \frac{dy}{dx}}$ =sec(x+y)? Answer: Put x+y=v, so that $1+{\displaystyle \frac{dy}{dx}}={\displaystyle \frac{dv}{dx}}$. ⇒ ${\displaystyle \frac{dy}{dx}}={\displaystyle \frac{dv}{dx}}-1$ … Read more

The general solution of the differential equation dy/dx=tan(x+y) is equal to y= x -log|cos(x+y) + sin(x+y)| +C where C denotes an arbitrary constant. In this post, we will learn how to solve the differential equation dy/dx = tan(x+y). General Solution of dy/dx=tan(x+y) Question: Find the general solution of ${\displaystyle \frac{dy}{dx}}$=tan(x+y). Solution: ${\displaystyle \frac{dy}{dx}}$=tan(x+y) ⇒ ${\displaystyle \frac{dy}{dx}}={\displaystyle \frac{\sin (x+y)}{\cos (x+y)}}$ … Read more

The solution of the differential equation dy/dx=1+x+y+xy is equal to y= 1 – $C{e}^{x+\frac{x^2}{2}}$ where C is an arbitrary constant. In this post, we will learn how to solve dy/dx=1+x+y+xy. Solution of dy/dx=1+x+y+xy Question: Solve the differential equation ${\displaystyle \frac{dy}{dx}}$ = 1+x+y+xy. Solution: We will solve solve ${\displaystyle \frac{dy}{dx}}$ =1+x+y+xy by variable separable method. The … Read more

The exact solution of dy/dx=x+y is equal to |x+y+1| = Cex where C is a constant. In this post, we will learn how to solve the differential equation dy/dx =x+y. Solve dy/dx=x+y Question: Find the general solution of ${\displaystyle \frac{dy}{dx}}=x+y$. Solution: To solve the given differential equation, we will use the substitute method. Let us put … Read more

The general solution of the differential equation dy/dx=cos(x+y) is equal to tan(x+y)/2 = x+C. Here we learn how to solve dy/dx=cos(x+y). Find General Solution of dy/dx=cos(x+y) Question: What is the solution of dy/dx=cos(x+y)? Answer: The solution of dy/dx=cos(x+y) is tan(x+y)/2 = x+C. Solution: Let x+y=2u So 1+ ${\displaystyle \frac{dy}{dx}}$ = 2 ${\displaystyle \frac{du}{dx}}$ ⇒ ${\displaystyle \frac{dy}{dx}}$ = 2 … Read more

The general solution of dy/dx=ex+y is equal to ex+ e-y= C, and the solution of dy/dx=ex-y is given by ex – ey= C. Here C denotes an arbitrary constant. Let us learn to solve dy/dx = e^(x+y) and dy/dx = e^(x-y), and find their general solutions. General Solution of dy/dx=ex+y Answer: The general solution of … Read more