Question

Solve the following differential equation: y dy/dx+tanh=2sinh

Answer 1

The provided differential equation to be solved by the student is incomplete or contains typos, and cannot be solved without further clarification or the correct form of the equation.

Step-by-step explanation:

The student has asked for help in solving a differential equation. Unfortunately, the differential equation provided appears to be incomplete or contains typos. Differential equations like this typically involve functions such as y, tanh (hyperbolic tangent), and sinh (hyperbolic sine), and could be solved through separation of variables, integration, or other methods depending on the full equation. To accurately solve the differential equation, we need all terms to be correctly written and the equation to be properly defined. Without the complete and correct form of the differential equation, it remains unsolvable, and I recommend asking for a clarification or the correct form of the differential equation.

The complete question is ..........Solve the following differential equation: y dy/dx+tanh=2sinh......../;

Answer 2

To solve the differential equation y dy/dx+tanh=2sinh, we need to separate the variables and integrate. Starting with the given equation, rearrange it to isolate the terms involving y and dy/dx. Next, integrate both sides of the equation. Simplify the integral and solve for y.

Step-by-step explanation:

To solve the differential equation y dy/dx+tanh=2sinh, we need to separate the variables and integrate.

Starting with the given equation, rearrange it to isolate the terms involving y and dy/dx.

y dy = (2sinh - tanh) dx

Next, integrate both sides of the equation.

(1/2) y^2 = ∫(2sinh - tanh) dx

Simplify the integral and solve for y.

y^2 = 2x sinh - ln|cosh(x)| + C

where C is the constant of integration.