Question

Given 3dy/dx+ 5y^2=sinx.y(0.3)=5 and using a step size of h = 0.3, the value of y(0.9) using Euler's method is most nearly​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given,

• equation $3\frac{dy}{dx}+5y^{2}=sinx$
• y(0.3) = 5
• step size of h = 0.3

To Find,

the value of y(0.9) using Euler's method.

Solution,

as this is given that $3\frac{dy}{dx}+5y^{2}=sinx$           (1)

y(0.3)=5

we have to find the value of y(0.9)

using equation (1)

$\frac{dy}{dx}=\frac{(sinx-5y^{2)} }{3}$                                                 (2)

Euler's method,

$x_{0} = 0.3 = y(0.3) , x_{1}= 0.6=y(0.6), x_{2}= 0.9=y(0.9)$

$y_{n+1} =y_{n} +h f(x_{n}.y_{n})$     , here n=0,1,2,3,....    (3)

putting n=1 in equation (3),

$y(0.9)= y_{2}=y_{1}+h(x_{1}.y_{1})$

         $= -7.470445+(0.3)(-92.75146)\\=-7.470445-27.825438\\= -35.295883\\= -35.318 (approx)$

Hence the value of y(0.9) is -35.318 (approx).