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 $\dfrac{dy}{dx}$=tan(x+y). Solution: $\dfrac{dy}{dx}$=tan(x+y) ⇒ $\dfrac{dy}{dx} = \dfrac{\sin(x+y)}{\cos(x+y)}$ … 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 $\dfrac{dy}{dx}$ = 1+x+y+xy. Solution: We will solve solve $\dfrac{dy}{dx}$ =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 $\dfrac{dy}{dx}=x+y$. 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+ $\dfrac{dy}{dx}$ = 2 $\dfrac{du}{dx}$ ⇒ $\dfrac{dy}{dx}$ = 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
The general solution of the differential equation dy/dx=sin(x+y) is given by tan(x+y) – sec(x+y) = x +C where C is an arbitrary constant. Here we will learn how to find the solution of dy/dx=sin(x+y). Let us now solve the differential equation dy/dx=sin(x+y) by the substitution method. General Solution of dy/dx=sin(x+y) Question: Find the general solution … Read more
The general solution of the differential equation dy/dx=x/y is given by y2 = x2 + C where C is an integral constant. Here we will learn how to find the solution of dy/dx=x/y. General Solution of dy/dx=x/y Question: Find the general solution of dy/dx=x/y. Answer: The given differential equation is $\dfrac{dy}{dx}=\dfrac{x}{y}$ Separating the variables x … Read more
The general solution of the differential equation dy/dx=y/x is given by y=cx where c is any constant. To solve dy/dx = y/x, we will use the separation of variables method. Let us learn how to find the solution of dy/dx=y/x. General Solution of dy/dx=y/x Question: Find the general solution of $\dfrac{dy}{dx}=\dfrac{y}{x}$. Answer: $\dfrac{dy}{dx}=\dfrac{y}{x}$ We can … Read more