Question

Find a function y(x) such that 5 y yʹ=x and y(5)=9

Answer 1

To find a function y(x) such that 5yyʹ=x and y(5)=9, we can start by separating the variables and integrating both sides of the equation.

Step-by-step explanation:

To find a function y(x) such that 5yyʹ=x and y(5)=9, we can start by separating the variables and integrating both sides of the equation. This gives us:

∫(1/5y) dy = ∫x dx

Solving the integrals, we get:
ln|y| = (1/2)x^2 + C

Next, we can exponentiate both sides to eliminate the logarithm:
|y|= e^((1/2)x^2 + C)

Since we have an initial condition y(5)=9, we can substitute these values into the equation and solve for C. After finding C, we can write the final function and simplify it further if necessary.