xy^3dx+e^{x^3}dy=0

해법

x y^{3} d x + e^{x^{3}} d y = 0

y = \frac{- 0 + 0 ^{2} - 4 \frac{1}{2} \cdot \frac{2}{3} \cdot 3 \cdot \frac{1}{2} - \frac{( 3 - ( x ^{2} ) ) ^{2} Γ ( \frac{1}{\frac{3}{2}} , - ( ( 3 - ( x ^{2} ) ) ^{2} ) ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - ( ( 3 - ( x ) ) ^{2} ) ^{\frac{3}{2}}} \cdot 2 + 2 c _{1} \cdot 1}{2 \frac{1}{2} \cdot \frac{2}{3} \cdot 3 \cdot \frac{1}{2} - \frac{( 3 - ( x ^{2} ) ^{\frac{3}{2}} ) ^{2} Γ ( \frac{1}{\frac{3}{2}} , - ( ( 3 - ( x ^{2} ) ^{\frac{3}{2}} ) ^{2} ) ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - ( ( 3 - ( x ^{2} ) ) ^{2} ) ^{\frac{3}{2}}} \cdot 2 + 2 c _{1}}, y = \frac{- 0 - 0 ^{2} - 4 \frac{1}{2} \cdot \frac{2}{3} \cdot 3 \cdot \frac{1}{2} - \frac{( 3 - ( x ^{2} ) ) ^{2} Γ ( \frac{1}{\frac{3}{2}} , - ( ( 3 - ( x ^{2} ) ) ^{2} ) ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - ( ( 3 - ( x ) ) ^{2} ) ^{\frac{3}{2}}} \cdot 2 + 2 c _{1} \cdot 1}{2 \frac{1}{2} \cdot \frac{2}{3} \cdot 3 \cdot \frac{1}{2} - \frac{( 3 - ( x ^{2} ) ^{\frac{3}{2}} ) ^{2} Γ ( \frac{1}{\frac{3}{2}} , - ( ( 3 - ( x ^{2} ) ^{\frac{3}{2}} ) ^{2} ) ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - ( ( 3 - ( x ^{2} ) ) ^{2} ) ^{\frac{3}{2}}} \cdot 2 + 2 c _{1}}

솔루션 단계

x y^{3} d x + e^{x^{3}} d y = 0

분리 가능한 ODE 해결:

y = \frac{- 0 + 0 ^{2} - 4 \frac{1}{2} \cdot \frac{2}{3} \cdot 3 \cdot \frac{1}{2} - \frac{( 3 - ( x ^{2} ) ) ^{2} Γ ( \frac{1}{\frac{3}{2}} , - ( ( 3 - ( x ^{2} ) ) ^{2} ) ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - ( ( 3 - ( x ) ) ^{2} ) ^{\frac{3}{2}}} \cdot 2 + 2 c _{1} \cdot 1}{2 \frac{1}{2} \cdot \frac{2}{3} \cdot 3 \cdot \frac{1}{2} - \frac{( 3 - ( x ^{2} ) ^{\frac{3}{2}} ) ^{2} Γ ( \frac{1}{\frac{3}{2}} , - ( ( 3 - ( x ^{2} ) ^{\frac{3}{2}} ) ^{2} ) ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - ( ( 3 - ( x ^{2} ) ) ^{2} ) ^{\frac{3}{2}}} \cdot 2 + 2 c _{1}}, y = \frac{- 0 - 0 ^{2} - 4 \frac{1}{2} \cdot \frac{2}{3} \cdot 3 \cdot \frac{1}{2} - \frac{( 3 - ( x ^{2} ) ) ^{2} Γ ( \frac{1}{\frac{3}{2}} , - ( ( 3 - ( x ^{2} ) ) ^{2} ) ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - ( ( 3 - ( x ) ) ^{2} ) ^{\frac{3}{2}}} \cdot 2 + 2 c _{1} \cdot 1}{2 \frac{1}{2} \cdot \frac{2}{3} \cdot 3 \cdot \frac{1}{2} - \frac{( 3 - ( x ^{2} ) ^{\frac{3}{2}} ) ^{2} Γ ( \frac{1}{\frac{3}{2}} , - ( ( 3 - ( x ^{2} ) ^{\frac{3}{2}} ) ^{2} ) ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - ( ( 3 - ( x ^{2} ) ) ^{2} ) ^{\frac{3}{2}}} \cdot 2 + 2 c _{1}}

y = \frac{- 0 + 0 ^{2} - 4 \frac{1}{2} \cdot \frac{2}{3} \cdot 3 \cdot \frac{1}{2} - \frac{( 3 - ( x ^{2} ) ) ^{2} Γ ( \frac{1}{\frac{3}{2}} , - ( ( 3 - ( x ^{2} ) ) ^{2} ) ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - ( ( 3 - ( x ) ) ^{2} ) ^{\frac{3}{2}}} \cdot 2 + 2 c _{1} \cdot 1}{2 \frac{1}{2} \cdot \frac{2}{3} \cdot 3 \cdot \frac{1}{2} - \frac{( 3 - ( x ^{2} ) ^{\frac{3}{2}} ) ^{2} Γ ( \frac{1}{\frac{3}{2}} , - ( ( 3 - ( x ^{2} ) ^{\frac{3}{2}} ) ^{2} ) ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - ( ( 3 - ( x ^{2} ) ) ^{2} ) ^{\frac{3}{2}}} \cdot 2 + 2 c _{1}}, y = \frac{- 0 - 0 ^{2} - 4 \frac{1}{2} \cdot \frac{2}{3} \cdot 3 \cdot \frac{1}{2} - \frac{( 3 - ( x ^{2} ) ) ^{2} Γ ( \frac{1}{\frac{3}{2}} , - ( ( 3 - ( x ^{2} ) ) ^{2} ) ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - ( ( 3 - ( x ) ) ^{2} ) ^{\frac{3}{2}}} \cdot 2 + 2 c _{1} \cdot 1}{2 \frac{1}{2} \cdot \frac{2}{3} \cdot 3 \cdot \frac{1}{2} - \frac{( 3 - ( x ^{2} ) ^{\frac{3}{2}} ) ^{2} Γ ( \frac{1}{\frac{3}{2}} , - ( ( 3 - ( x ^{2} ) ^{\frac{3}{2}} ) ^{2} ) ^{\frac{3}{2}} )}{\frac{3}{2} \frac{3}{2} - ( ( 3 - ( x ^{2} ) ) ^{2} ) ^{\frac{3}{2}}} \cdot 2 + 2 c _{1}}