What is the solution for 49y^{''}-126y^'+117y=0,y(4)=2,y^'(4)=2 ?

The solution for 49y^{''}-126y^'+117y=0,y(4)=2,y^'(4)=2 is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

49y^{''}-126y^'+117y=0,y(4)=2,y^'(4)=2

49 y^{^{''}} - 126 y^{^{'}} + 117 y = 0, y (4) = 2, y^{^{'}} (4) = 2

y = e^{\frac{9 t}{7}} (\frac{( 12 ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) ) - sin ( \frac{24}{7} ) ( 12 sin ( \frac{24}{7} ) - 4 cos ( \frac{24}{7} ) ) ) cos ( \frac{6 t}{7} )}{6 e ^{\frac{36}{7}} cos ( \frac{24}{7} ) ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) )} + \frac{( 12 sin ( \frac{24}{7} ) - 4 cos ( \frac{24}{7} ) ) sin ( \frac{6 t}{7} )}{6 e ^{\frac{36}{7}} ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) )})

Solution steps

49 y^{''} (t) - 126 y^{'} (t) + 117 y = 0

Solve linear ODE:

y = e^{\frac{9 t}{7}} (\frac{( 12 ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) ) - sin ( \frac{24}{7} ) ( 12 sin ( \frac{24}{7} ) - 4 cos ( \frac{24}{7} ) ) ) cos ( \frac{6 t}{7} )}{6 e ^{\frac{36}{7}} cos ( \frac{24}{7} ) ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) )} + \frac{( 12 sin ( \frac{24}{7} ) - 4 cos ( \frac{24}{7} ) ) sin ( \frac{6 t}{7} )}{6 e ^{\frac{36}{7}} ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) )})

y = e^{\frac{9 t}{7}} (\frac{( 12 ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) ) - sin ( \frac{24}{7} ) ( 12 sin ( \frac{24}{7} ) - 4 cos ( \frac{24}{7} ) ) ) cos ( \frac{6 t}{7} )}{6 e ^{\frac{36}{7}} cos ( \frac{24}{7} ) ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) )} + \frac{( 12 sin ( \frac{24}{7} ) - 4 cos ( \frac{24}{7} ) ) sin ( \frac{6 t}{7} )}{6 e ^{\frac{36}{7}} ( cos ^{2} ( \frac{24}{7} ) + sin ^{2} ( \frac{24}{7} ) )})

y^{^{''}} - 3 y^{^{'}} = 0, y (0) = 6 - 6 e^{3}, y (1) = 0

2 y^{^{''}} - 10 y^{^{'}} + 12 y = 0

y^{^{'''}} - 3 y^{^{''}} - 49 y^{^{'}} - 45 y = 0

y^{^{''}} + 5 y^{^{'}} + 6 y = 0, y (0) = 6, y^{^{'}} (0) = - 8

16 y^{^{''}} - 40 y^{^{'}} - 25 y = 0

What is the solution for 49y^{''}-126y^'+117y=0,y(4)=2,y^'(4)=2 ?
The solution for 49y^{''}-126y^'+117y=0,y(4)=2,y^'(4)=2 is